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<a class="navbar-brand"><b>QuEST</b> v3.4.0<br>The Quantum Exact Simulation Toolkit</a>
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<a href="#func-members">Functions</a> </div>
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<div class="title">Unitaries</div> </div>
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<p>Unitary gates.
<a href="#details">More...</a></p>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:gaefaa7acba90373efe4e0f0b94987c734"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gaefaa7acba90373efe4e0f0b94987c734">compactUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit, <a class="el" href="structComplex.html">Complex</a> alpha, <a class="el" href="structComplex.html">Complex</a> beta)</td></tr>
<tr class="memdesc:gaefaa7acba90373efe4e0f0b94987c734"><td class="mdescLeft"> </td><td class="mdescRight">Apply a single-qubit unitary parameterised by two given complex scalars. <a href="group__unitary.html#gaefaa7acba90373efe4e0f0b94987c734">More...</a><br /></td></tr>
<tr class="separator:gaefaa7acba90373efe4e0f0b94987c734"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaf7e15bf09c64082e0a8467998eb25623"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gaf7e15bf09c64082e0a8467998eb25623">controlledCompactUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit, <a class="el" href="structComplex.html">Complex</a> alpha, <a class="el" href="structComplex.html">Complex</a> beta)</td></tr>
<tr class="memdesc:gaf7e15bf09c64082e0a8467998eb25623"><td class="mdescLeft"> </td><td class="mdescRight">Apply a controlled unitary (single control, single target) parameterised by two given complex scalars. <a href="group__unitary.html#gaf7e15bf09c64082e0a8467998eb25623">More...</a><br /></td></tr>
<tr class="separator:gaf7e15bf09c64082e0a8467998eb25623"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaeb975903209000ebbaf50ef1cc353a79"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gaeb975903209000ebbaf50ef1cc353a79">controlledMultiQubitUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int ctrl, int *targs, int numTargs, <a class="el" href="structComplexMatrixN.html">ComplexMatrixN</a> u)</td></tr>
<tr class="memdesc:gaeb975903209000ebbaf50ef1cc353a79"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general controlled multi-qubit unitary (including a global phase factor). <a href="group__unitary.html#gaeb975903209000ebbaf50ef1cc353a79">More...</a><br /></td></tr>
<tr class="separator:gaeb975903209000ebbaf50ef1cc353a79"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaa5a138473a4433c853c6e66e7aabc237"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gaa5a138473a4433c853c6e66e7aabc237">controlledNot</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit)</td></tr>
<tr class="memdesc:gaa5a138473a4433c853c6e66e7aabc237"><td class="mdescLeft"> </td><td class="mdescRight">Apply the controlled not (single control, single target) gate, also known as the c-X, c-sigma-X, c-Pauli-X and c-bit-flip gate. <a href="group__unitary.html#gaa5a138473a4433c853c6e66e7aabc237">More...</a><br /></td></tr>
<tr class="separator:gaa5a138473a4433c853c6e66e7aabc237"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga5e5fdaa7d3dd449b3e2c5d4a01bd015a"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga5e5fdaa7d3dd449b3e2c5d4a01bd015a">controlledPauliY</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit)</td></tr>
<tr class="memdesc:ga5e5fdaa7d3dd449b3e2c5d4a01bd015a"><td class="mdescLeft"> </td><td class="mdescRight">Apply the controlled pauliY (single control, single target) gate, also known as the c-Y and c-sigma-Y gate. <a href="group__unitary.html#ga5e5fdaa7d3dd449b3e2c5d4a01bd015a">More...</a><br /></td></tr>
<tr class="separator:ga5e5fdaa7d3dd449b3e2c5d4a01bd015a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga2fa310101ecffd6aeba96f77b7d85f56"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga2fa310101ecffd6aeba96f77b7d85f56">controlledPhaseFlip</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int idQubit1, int idQubit2)</td></tr>
<tr class="memdesc:ga2fa310101ecffd6aeba96f77b7d85f56"><td class="mdescLeft"> </td><td class="mdescRight">Apply the (two-qubit) controlled phase flip gate, also known as the controlled pauliZ gate. <a href="group__unitary.html#ga2fa310101ecffd6aeba96f77b7d85f56">More...</a><br /></td></tr>
<tr class="separator:ga2fa310101ecffd6aeba96f77b7d85f56"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga7214a79aa22ae7a50ad6f38615968cb0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0">controlledPhaseShift</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int idQubit1, int idQubit2, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga7214a79aa22ae7a50ad6f38615968cb0"><td class="mdescLeft"> </td><td class="mdescRight">Introduce a phase factor <img class="formulaInl" alt="$ \exp(i \theta) $" src="form_67.png"/> on state <img class="formulaInl" alt="$ |11\rangle $" src="form_68.png"/> of qubits <code>idQubit1</code> and <code>idQubit2</code>. <a href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0">More...</a><br /></td></tr>
<tr class="separator:ga7214a79aa22ae7a50ad6f38615968cb0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga0c84c429cb1d7e2596706c1804dd9cba"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga0c84c429cb1d7e2596706c1804dd9cba">controlledRotateAroundAxis</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle, <a class="el" href="structVector.html">Vector</a> axis)</td></tr>
<tr class="memdesc:ga0c84c429cb1d7e2596706c1804dd9cba"><td class="mdescLeft"> </td><td class="mdescRight">Applies a controlled rotation by a given angle around a given vector on the Bloch-sphere. <a href="group__unitary.html#ga0c84c429cb1d7e2596706c1804dd9cba">More...</a><br /></td></tr>
<tr class="separator:ga0c84c429cb1d7e2596706c1804dd9cba"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga13f904b417f647c70d163770e65906fc"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga13f904b417f647c70d163770e65906fc">controlledRotateX</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga13f904b417f647c70d163770e65906fc"><td class="mdescLeft"> </td><td class="mdescRight">Applies a controlled rotation by a given angle around the X-axis of the Bloch-sphere. <a href="group__unitary.html#ga13f904b417f647c70d163770e65906fc">More...</a><br /></td></tr>
<tr class="separator:ga13f904b417f647c70d163770e65906fc"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gafbbded98b7233f5da06d74d1db5cbfdb"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gafbbded98b7233f5da06d74d1db5cbfdb">controlledRotateY</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:gafbbded98b7233f5da06d74d1db5cbfdb"><td class="mdescLeft"> </td><td class="mdescRight">Applies a controlled rotation by a given angle around the Y-axis of the Bloch-sphere. <a href="group__unitary.html#gafbbded98b7233f5da06d74d1db5cbfdb">More...</a><br /></td></tr>
<tr class="separator:gafbbded98b7233f5da06d74d1db5cbfdb"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga7eb969c1dd6c949aecf716d2fba71120"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120">controlledRotateZ</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga7eb969c1dd6c949aecf716d2fba71120"><td class="mdescLeft"> </td><td class="mdescRight">Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere. <a href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120">More...</a><br /></td></tr>
<tr class="separator:ga7eb969c1dd6c949aecf716d2fba71120"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga3d89916b46bc4aaf23e938022e6c89c1"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga3d89916b46bc4aaf23e938022e6c89c1">controlledTwoQubitUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit1, int targetQubit2, <a class="el" href="structComplexMatrix4.html">ComplexMatrix4</a> u)</td></tr>
<tr class="memdesc:ga3d89916b46bc4aaf23e938022e6c89c1"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general controlled two-qubit unitary (including a global phase factor). <a href="group__unitary.html#ga3d89916b46bc4aaf23e938022e6c89c1">More...</a><br /></td></tr>
<tr class="separator:ga3d89916b46bc4aaf23e938022e6c89c1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaa3fb996a5cadd098f4acd8aec955cf9c"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gaa3fb996a5cadd098f4acd8aec955cf9c">controlledUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int controlQubit, int targetQubit, <a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> u)</td></tr>
<tr class="memdesc:gaa3fb996a5cadd098f4acd8aec955cf9c"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general controlled unitary (single control, single target), which can include a global phase factor. <a href="group__unitary.html#gaa3fb996a5cadd098f4acd8aec955cf9c">More...</a><br /></td></tr>
<tr class="separator:gaa3fb996a5cadd098f4acd8aec955cf9c"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga6532decd6c404189915563492f090e6f"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga6532decd6c404189915563492f090e6f">hadamard</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit)</td></tr>
<tr class="memdesc:ga6532decd6c404189915563492f090e6f"><td class="mdescLeft"> </td><td class="mdescRight">Apply the single-qubit Hadamard gate. <a href="group__unitary.html#ga6532decd6c404189915563492f090e6f">More...</a><br /></td></tr>
<tr class="separator:ga6532decd6c404189915563492f090e6f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gafd81a9217fb7d21c365443442492b2dc"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gafd81a9217fb7d21c365443442492b2dc">multiControlledMultiQubitNot</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *ctrls, int numCtrls, int *targs, int numTargs)</td></tr>
<tr class="memdesc:gafd81a9217fb7d21c365443442492b2dc"><td class="mdescLeft"> </td><td class="mdescRight">Apply a NOT (or Pauli X) gate with multiple control and target qubits. <a href="group__unitary.html#gafd81a9217fb7d21c365443442492b2dc">More...</a><br /></td></tr>
<tr class="separator:gafd81a9217fb7d21c365443442492b2dc"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga3ad6c477edcdbc845fc1143e860fda08"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga3ad6c477edcdbc845fc1143e860fda08">multiControlledMultiQubitUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *ctrls, int numCtrls, int *targs, int numTargs, <a class="el" href="structComplexMatrixN.html">ComplexMatrixN</a> u)</td></tr>
<tr class="memdesc:ga3ad6c477edcdbc845fc1143e860fda08"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general multi-controlled multi-qubit unitary (including a global phase factor). <a href="group__unitary.html#ga3ad6c477edcdbc845fc1143e860fda08">More...</a><br /></td></tr>
<tr class="separator:ga3ad6c477edcdbc845fc1143e860fda08"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gab2ececaa253252e1b1cdb18a8452704a"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gab2ececaa253252e1b1cdb18a8452704a">multiControlledMultiRotatePauli</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int numControls, int *targetQubits, enum <a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028">pauliOpType</a> *targetPaulis, int numTargets, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:gab2ececaa253252e1b1cdb18a8452704a"><td class="mdescLeft"> </td><td class="mdescRight">Apply a multi-controlled multi-target multi-Pauli rotation, also known as a controlled Pauli gadget. <a href="group__unitary.html#gab2ececaa253252e1b1cdb18a8452704a">More...</a><br /></td></tr>
<tr class="separator:gab2ececaa253252e1b1cdb18a8452704a"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga1e5dd165b402e97abaa0b807026527f2"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga1e5dd165b402e97abaa0b807026527f2">multiControlledMultiRotateZ</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int numControls, int *targetQubits, int numTargets, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga1e5dd165b402e97abaa0b807026527f2"><td class="mdescLeft"> </td><td class="mdescRight">Apply a multi-controlled multi-target Z rotation, also known as a controlled phase gadget. <a href="group__unitary.html#ga1e5dd165b402e97abaa0b807026527f2">More...</a><br /></td></tr>
<tr class="separator:ga1e5dd165b402e97abaa0b807026527f2"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gad76781842af56821ed4e223bd776f057"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gad76781842af56821ed4e223bd776f057">multiControlledPhaseFlip</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int numControlQubits)</td></tr>
<tr class="memdesc:gad76781842af56821ed4e223bd776f057"><td class="mdescLeft"> </td><td class="mdescRight">Apply the multiple-qubit controlled phase flip gate, also known as the multiple-qubit controlled pauliZ gate. <a href="group__unitary.html#gad76781842af56821ed4e223bd776f057">More...</a><br /></td></tr>
<tr class="separator:gad76781842af56821ed4e223bd776f057"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga0832e39058d913ad47af44e97a854446"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga0832e39058d913ad47af44e97a854446">multiControlledPhaseShift</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int numControlQubits, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga0832e39058d913ad47af44e97a854446"><td class="mdescLeft"> </td><td class="mdescRight">Introduce a phase factor <img class="formulaInl" alt="$ \exp(i \theta) $" src="form_67.png"/> on state <img class="formulaInl" alt="$ |1 \dots 1 \rangle $" src="form_71.png"/> of the passed qubits. <a href="group__unitary.html#ga0832e39058d913ad47af44e97a854446">More...</a><br /></td></tr>
<tr class="separator:ga0832e39058d913ad47af44e97a854446"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga65c7879947e398690a5428bd43e143e3"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga65c7879947e398690a5428bd43e143e3">multiControlledTwoQubitUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int numControlQubits, int targetQubit1, int targetQubit2, <a class="el" href="structComplexMatrix4.html">ComplexMatrix4</a> u)</td></tr>
<tr class="memdesc:ga65c7879947e398690a5428bd43e143e3"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general multi-controlled two-qubit unitary (including a global phase factor). <a href="group__unitary.html#ga65c7879947e398690a5428bd43e143e3">More...</a><br /></td></tr>
<tr class="separator:ga65c7879947e398690a5428bd43e143e3"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gaa700dc9657ade4cf16f1cad1624c5332"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332">multiControlledUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int numControlQubits, int targetQubit, <a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> u)</td></tr>
<tr class="memdesc:gaa700dc9657ade4cf16f1cad1624c5332"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general multiple-control single-target unitary, which can include a global phase factor. <a href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332">More...</a><br /></td></tr>
<tr class="separator:gaa700dc9657ade4cf16f1cad1624c5332"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga7e58e8131f219f48e5b7410ca8dfe0c0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga7e58e8131f219f48e5b7410ca8dfe0c0">multiQubitNot</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *targs, int numTargs)</td></tr>
<tr class="memdesc:ga7e58e8131f219f48e5b7410ca8dfe0c0"><td class="mdescLeft"> </td><td class="mdescRight">Apply a NOT (or Pauli X) gate with multiple target qubits, which has the same effect as (but is much faster than) applying each single-qubit NOT gate in turn. <a href="group__unitary.html#ga7e58e8131f219f48e5b7410ca8dfe0c0">More...</a><br /></td></tr>
<tr class="separator:ga7e58e8131f219f48e5b7410ca8dfe0c0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga20bf9b8a71b8a3ee4651e9497e6d1f4f"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f">multiQubitUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *targs, int numTargs, <a class="el" href="structComplexMatrixN.html">ComplexMatrixN</a> u)</td></tr>
<tr class="memdesc:ga20bf9b8a71b8a3ee4651e9497e6d1f4f"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubits. <a href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f">More...</a><br /></td></tr>
<tr class="separator:ga20bf9b8a71b8a3ee4651e9497e6d1f4f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga34aa4865c92f9aa5d898c91286c9eca5"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5">multiRotatePauli</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *targetQubits, enum <a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028">pauliOpType</a> *targetPaulis, int numTargets, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga34aa4865c92f9aa5d898c91286c9eca5"><td class="mdescLeft"> </td><td class="mdescRight">Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubits. <a href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5">More...</a><br /></td></tr>
<tr class="separator:ga34aa4865c92f9aa5d898c91286c9eca5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga3250d0d95b5d755cad542a6a2372b894"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894">multiRotateZ</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *qubits, int numQubits, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga3250d0d95b5d755cad542a6a2372b894"><td class="mdescLeft"> </td><td class="mdescRight">Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits. <a href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894">More...</a><br /></td></tr>
<tr class="separator:ga3250d0d95b5d755cad542a6a2372b894"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga41b946a82982c3fa3dc2a7395665bc90"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga41b946a82982c3fa3dc2a7395665bc90">multiStateControlledUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int *controlQubits, int *controlState, int numControlQubits, int targetQubit, <a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> u)</td></tr>
<tr class="memdesc:ga41b946a82982c3fa3dc2a7395665bc90"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general single-qubit unitary with multiple control qubits, conditioned upon a specific bit sequence. <a href="group__unitary.html#ga41b946a82982c3fa3dc2a7395665bc90">More...</a><br /></td></tr>
<tr class="separator:ga41b946a82982c3fa3dc2a7395665bc90"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga4193c14cfb918fa3291fb0648058d63e"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e">pauliX</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit)</td></tr>
<tr class="memdesc:ga4193c14cfb918fa3291fb0648058d63e"><td class="mdescLeft"> </td><td class="mdescRight">Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate. <a href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e">More...</a><br /></td></tr>
<tr class="separator:ga4193c14cfb918fa3291fb0648058d63e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga8e0f03e745778a89d6f59c3c25e32df8"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga8e0f03e745778a89d6f59c3c25e32df8">pauliY</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit)</td></tr>
<tr class="memdesc:ga8e0f03e745778a89d6f59c3c25e32df8"><td class="mdescLeft"> </td><td class="mdescRight">Apply the single-qubit Pauli-Y (also known as the Y or sigma-Y) gate. <a href="group__unitary.html#ga8e0f03e745778a89d6f59c3c25e32df8">More...</a><br /></td></tr>
<tr class="separator:ga8e0f03e745778a89d6f59c3c25e32df8"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga5d80b490e3910aa737a81bb597cdfcc9"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga5d80b490e3910aa737a81bb597cdfcc9">pauliZ</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit)</td></tr>
<tr class="memdesc:ga5d80b490e3910aa737a81bb597cdfcc9"><td class="mdescLeft"> </td><td class="mdescRight">Apply the single-qubit Pauli-Z (also known as the Z, sigma-Z or phase-flip) gate. <a href="group__unitary.html#ga5d80b490e3910aa737a81bb597cdfcc9">More...</a><br /></td></tr>
<tr class="separator:ga5d80b490e3910aa737a81bb597cdfcc9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga26baa057f5db8804825c2d611386753b"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga26baa057f5db8804825c2d611386753b">phaseShift</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga26baa057f5db8804825c2d611386753b"><td class="mdescLeft"> </td><td class="mdescRight">Shift the phase between <img class="formulaInl" alt="$ |0\rangle $" src="form_62.png"/> and <img class="formulaInl" alt="$ |1\rangle $" src="form_63.png"/> of a single qubit by a given angle. <a href="group__unitary.html#ga26baa057f5db8804825c2d611386753b">More...</a><br /></td></tr>
<tr class="separator:ga26baa057f5db8804825c2d611386753b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga4c708f066b244801e10f538b48b90145"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145">rotateAroundAxis</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int rotQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle, <a class="el" href="structVector.html">Vector</a> axis)</td></tr>
<tr class="memdesc:ga4c708f066b244801e10f538b48b90145"><td class="mdescLeft"> </td><td class="mdescRight">Rotate a single qubit by a given angle around a given <a class="el" href="structVector.html">Vector</a> on the Bloch-sphere. <a href="group__unitary.html#ga4c708f066b244801e10f538b48b90145">More...</a><br /></td></tr>
<tr class="separator:ga4c708f066b244801e10f538b48b90145"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga8886a3793b21622c48cf3bad6e15082d"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d">rotateX</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int rotQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga8886a3793b21622c48cf3bad6e15082d"><td class="mdescLeft"> </td><td class="mdescRight">Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere. <a href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d">More...</a><br /></td></tr>
<tr class="separator:ga8886a3793b21622c48cf3bad6e15082d"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga34312ff52cc28bcab3cbd2ff338fd081"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081">rotateY</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int rotQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:ga34312ff52cc28bcab3cbd2ff338fd081"><td class="mdescLeft"> </td><td class="mdescRight">Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere. <a href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081">More...</a><br /></td></tr>
<tr class="separator:ga34312ff52cc28bcab3cbd2ff338fd081"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gab23a8b022ec83b9d423961ca87cd8cb5"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5">rotateZ</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int rotQubit, <a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> angle)</td></tr>
<tr class="memdesc:gab23a8b022ec83b9d423961ca87cd8cb5"><td class="mdescLeft"> </td><td class="mdescRight">Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase shift gate). <a href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5">More...</a><br /></td></tr>
<tr class="separator:gab23a8b022ec83b9d423961ca87cd8cb5"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga655ffcd4def2e127341c9488f5ca8455"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga655ffcd4def2e127341c9488f5ca8455">sGate</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit)</td></tr>
<tr class="memdesc:ga655ffcd4def2e127341c9488f5ca8455"><td class="mdescLeft"> </td><td class="mdescRight">Apply the single-qubit S gate. <a href="group__unitary.html#ga655ffcd4def2e127341c9488f5ca8455">More...</a><br /></td></tr>
<tr class="separator:ga655ffcd4def2e127341c9488f5ca8455"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga75d5e65f87c68403602a669b9c6d52b0"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga75d5e65f87c68403602a669b9c6d52b0">sqrtSwapGate</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int qb1, int qb2)</td></tr>
<tr class="memdesc:ga75d5e65f87c68403602a669b9c6d52b0"><td class="mdescLeft"> </td><td class="mdescRight">Performs a sqrt SWAP gate between <code>qubit1</code> and <code>qubit2</code>. <a href="group__unitary.html#ga75d5e65f87c68403602a669b9c6d52b0">More...</a><br /></td></tr>
<tr class="separator:ga75d5e65f87c68403602a669b9c6d52b0"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga820fd139c035136819e371308c206e36"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga820fd139c035136819e371308c206e36">swapGate</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int qubit1, int qubit2)</td></tr>
<tr class="memdesc:ga820fd139c035136819e371308c206e36"><td class="mdescLeft"> </td><td class="mdescRight">Performs a SWAP gate between <code>qubit1</code> and <code>qubit2</code>. <a href="group__unitary.html#ga820fd139c035136819e371308c206e36">More...</a><br /></td></tr>
<tr class="separator:ga820fd139c035136819e371308c206e36"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gac15907193da5a7c48b9610a26e669064"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gac15907193da5a7c48b9610a26e669064">tGate</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit)</td></tr>
<tr class="memdesc:gac15907193da5a7c48b9610a26e669064"><td class="mdescLeft"> </td><td class="mdescRight">Apply the single-qubit T gate. <a href="group__unitary.html#gac15907193da5a7c48b9610a26e669064">More...</a><br /></td></tr>
<tr class="separator:gac15907193da5a7c48b9610a26e669064"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:gab525a42d63233f61afeb6be97d89dd36"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36">twoQubitUnitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit1, int targetQubit2, <a class="el" href="structComplexMatrix4.html">ComplexMatrix4</a> u)</td></tr>
<tr class="memdesc:gab525a42d63233f61afeb6be97d89dd36"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general two-qubit unitary (including a global phase factor). <a href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36">More...</a><br /></td></tr>
<tr class="separator:gab525a42d63233f61afeb6be97d89dd36"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ga78b814256f851cac70fdf3cbf9cfc206"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206">unitary</a> (<a class="el" href="structQureg.html">Qureg</a> qureg, int targetQubit, <a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> u)</td></tr>
<tr class="memdesc:ga78b814256f851cac70fdf3cbf9cfc206"><td class="mdescLeft"> </td><td class="mdescRight">Apply a general single-qubit unitary (including a global phase factor). <a href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206">More...</a><br /></td></tr>
<tr class="separator:ga78b814256f851cac70fdf3cbf9cfc206"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<p>Unitary gates. </p>
<h2 class="groupheader">Function Documentation</h2>
<a id="gaefaa7acba90373efe4e0f0b94987c734"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gaefaa7acba90373efe4e0f0b94987c734">◆ </a></span>compactUnitary()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void compactUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplex.html">Complex</a> </td>
<td class="paramname"><em>alpha</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplex.html">Complex</a> </td>
<td class="paramname"><em>beta</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a single-qubit unitary parameterised by two given complex scalars. </p>
<p>Given valid complex numbers <img class="formulaInl" alt="$\alpha$" src="form_88.png"/> and <img class="formulaInl" alt="$\beta$" src="form_89.png"/>, applies the unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ U = \begin{pmatrix} \alpha & -\beta^* \\ \beta & \alpha^* \end{pmatrix} \]" src="form_90.png"/>
</p>
<p> which is general up to a global phase factor. <br />
Valid <img class="formulaInl" alt="$\alpha$" src="form_88.png"/>, <img class="formulaInl" alt="$\beta$" src="form_89.png"/> satisfy <img class="formulaInl" alt="$|\alpha|^2 + |\beta|^2 = 1$" src="form_91.png"/>.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {U}; \end{tikzpicture} \]" src="form_92.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gaf7e15bf09c64082e0a8467998eb25623" title="Apply a controlled unitary (single control, single target) parameterised by two given complex scalars...">controlledCompactUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">alpha</td><td>complex unitary parameter (row 1, column 1) </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">beta</td><td>complex unitary parameter (row 2, column 1) </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>alpha</code>, <code>beta</code> don't satisfy |<code>alpha</code>|^2 + |<code>beta</code>|^2 = 1 </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00404">404</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  {</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>  <a class="code" href="QuEST__validation_8c.html#a5d49d4aadea858794b139c6a195ffd8b">validateUnitaryComplexPair</a>(alpha, beta, __func__);</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  </div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <a class="code" href="QuEST__internal_8h.html#aec63559e8b9ab0e17efe18d64d2ceca6">statevec_compactUnitary</a>(qureg, targetQubit, alpha, beta);</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <a class="code" href="QuEST__internal_8h.html#aec63559e8b9ab0e17efe18d64d2ceca6">statevec_compactUnitary</a>(qureg, targetQubit+shift, <a class="code" href="QuEST__common_8c.html#af92fa737f4491324408b3d15543dced4">getConjugateScalar</a>(alpha), <a class="code" href="QuEST__common_8c.html#af92fa737f4491324408b3d15543dced4">getConjugateScalar</a>(beta));</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  }</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  </div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <a class="code" href="QuEST__qasm_8c.html#a518c4351d574aea8477019dbce02f09c">qasm_recordCompactUnitary</a>(qureg, alpha, beta, targetQubit);</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00091">getConjugateScalar()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00196">qasm_recordCompactUnitary()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l00858">statevec_compactUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00507">validateUnitaryComplexPair()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00046">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gaf7e15bf09c64082e0a8467998eb25623"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gaf7e15bf09c64082e0a8467998eb25623">◆ </a></span>controlledCompactUnitary()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void controlledCompactUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplex.html">Complex</a> </td>
<td class="paramname"><em>alpha</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplex.html">Complex</a> </td>
<td class="paramname"><em>beta</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply a controlled unitary (single control, single target) parameterised by two given complex scalars. </p>
<p>Given valid complex numbers <img class="formulaInl" alt="$\alpha$" src="form_88.png"/> and <img class="formulaInl" alt="$\beta$" src="form_89.png"/>, applies the two-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\ & & \alpha & -\beta^* \\ & & \beta & \alpha^* \end{pmatrix} \]" src="form_108.png"/>
</p>
<p> to the control and target qubits. Valid <img class="formulaInl" alt="$\alpha$" src="form_88.png"/>, <img class="formulaInl" alt="$\beta$" src="form_89.png"/> satisfy <img class="formulaInl" alt="$|\alpha|^2 + |\beta|^2 = 1$" src="form_91.png"/>. The target unitary is general up to a global phase factor. <br />
</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$U_{\alpha, \beta}$}; \end{tikzpicture} \]" src="form_109.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gaefaa7acba90373efe4e0f0b94987c734" title="Apply a single-qubit unitary parameterised by two given complex scalars.">compactUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa3fb996a5cadd098f4acd8aec955cf9c" title="Apply a general controlled unitary (single control, single target), which can include a global phase ...">controlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332" title="Apply a general multiple-control single-target unitary, which can include a global phase factor.">multiControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga41b946a82982c3fa3dc2a7395665bc90" title="Apply a general single-qubit unitary with multiple control qubits, conditioned upon a specific bit se...">multiStateControlledUnitary()</a></li>
</ul>
</dd></dl>
<p><br />
</p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>apply the target unitary if this qubit has value 1 </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit on which to apply the target unitary </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">alpha</td><td>complex unitary parameter (row 1, column 1) </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">beta</td><td>complex unitary parameter (row 2, column 1) </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal</li>
<li>if <code>alpha</code>, <code>beta</code> don't satisfy |<code>alpha</code>|^2 + |<code>beta</code>|^2 = 1 </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00417">417</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  {</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  <a class="code" href="QuEST__validation_8c.html#a5d49d4aadea858794b139c6a195ffd8b">validateUnitaryComplexPair</a>(alpha, beta, __func__);</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <a class="code" href="QuEST__internal_8h.html#a1275d604674224d87a173fb5bac78835">statevec_controlledCompactUnitary</a>(qureg, controlQubit, targetQubit, alpha, beta);</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>  <a class="code" href="QuEST__internal_8h.html#a1275d604674224d87a173fb5bac78835">statevec_controlledCompactUnitary</a>(qureg, </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  controlQubit+shift, targetQubit+shift, </div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  <a class="code" href="QuEST__common_8c.html#af92fa737f4491324408b3d15543dced4">getConjugateScalar</a>(alpha), <a class="code" href="QuEST__common_8c.html#af92fa737f4491324408b3d15543dced4">getConjugateScalar</a>(beta));</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>  }</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  </div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <a class="code" href="QuEST__qasm_8c.html#a6bd68fa9c0c1bd9c9f9af714ea0b8b03">qasm_recordControlledCompactUnitary</a>(qureg, alpha, beta, controlQubit, targetQubit);</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00091">getConjugateScalar()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00265">qasm_recordControlledCompactUnitary()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l00934">statevec_controlledCompactUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00507">validateUnitaryComplexPair()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00097">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gaeb975903209000ebbaf50ef1cc353a79"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gaeb975903209000ebbaf50ef1cc353a79">◆ </a></span>controlledMultiQubitUnitary()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">void controlledMultiQubitUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>ctrl</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrixN.html">ComplexMatrixN</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a general controlled multi-qubit unitary (including a global phase factor). </p>
<p>One control and any number of target qubits can be specified. This effects the many-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & 1 \\ & & & 1 \\ & & & & u_{00} & u_{01} & \dots \\ & & & & u_{10} & u_{11} & \dots \\ & & & & \vdots & \vdots & \ddots \end{pmatrix} \]" src="form_219.png"/>
</p>
<p> on the control and target qubits.</p>
<p>The target qubits in <code>targs</code> are treated as ordered least significant to most significant in <code>u</code>.</p>
<p>The passed ComplexMatrix must be unitary and be a compatible size with the specified number of target qubits, otherwise an error is thrown.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 1) {targets}; \node[draw=none] at (-3.5, 4) {control}; \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, 3); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-2,2) -- (-1, 2); \draw (1, 2) -- (2, 2); \draw (-1,-1)--(-1,3)--(1,3)--(1,-1); \node[draw=none] at (0, 1) {U}; \node[draw=none] at (0, -1) {$\vdots$}; \end{tikzpicture} \]" src="form_220.png"/>
</p>
<p>Note that in multithreaded mode, each thread will clone 2^<code>numTargs</code> amplitudes, and store these in the runtime stack. Using t threads, the total memory overhead of this function is t*2^<code>numTargs</code>. For many targets (e.g. 16 qubits), this may cause a stack-overflow / seg-fault (e.g. on a 1 MiB stack).</p>
<p>Note too that in distributed mode, this routine requires that each node contains at least 2^<code>numTargs</code> amplitudes. This means an q-qubit register (state vector or density matrix) can be distributed by at most 2^q / 2^<code>numTargs</code> nodes.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__type.html#ga815103261fb22ea9690e1427571df00e" title="Allocate dynamic memory for a square complex matrix of any size, which can be passed to functions lik...">createComplexMatrixN()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga3ad6c477edcdbc845fc1143e860fda08" title="Apply a general multi-controlled multi-qubit unitary (including a global phase factor).">multiControlledMultiQubitUnitary()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">ctrl</td><td>the control qubit </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targs</td><td>a list of the target qubits, ordered least to most significant </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargs</td><td>the number of target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>ctrl</code> or any index in <code>targs</code> is outside of [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>targs</code> are not unique</li>
<li>if <code>targs</code> contains <code>ctrl</code> </li>
<li>if matrix <code>u</code> is not unitary</li>
<li>if a node cannot fit the required number of target amplitudes in distributed mode </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00313">313</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  {</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, (<span class="keywordtype">int</span>[]) {ctrl}, 1, targs, numTargs, __func__);</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <a class="code" href="QuEST__validation_8c.html#ab9947ff071a0c019f715f04b3833dcfd">validateMultiQubitUnitaryMatrix</a>(qureg, u, numTargs, __func__);</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  </div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <a class="code" href="QuEST__common_8c.html#a06b8474aec51579ff680fb66439e7fc6">statevec_controlledMultiQubitUnitary</a>(qureg, ctrl, targs, numTargs, u);</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targs, numTargs, shift);</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <a class="code" href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a>(u);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <a class="code" href="QuEST__common_8c.html#a06b8474aec51579ff680fb66439e7fc6">statevec_controlledMultiQubitUnitary</a>(qureg, ctrl+shift, targs, numTargs, u);</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targs, numTargs, -shift);</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <a class="code" href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a>(u);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  }</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  </div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, <span class="stringliteral">"Here, an undisclosed controlled multi-qubit unitary was applied."</span>);</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00115">setConjugateMatrixN()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__common_8c_source.html#l00579">statevec_controlledMultiQubitUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00502">validateMultiQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00155">TEST_CASE()</a>.</p>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gaa5a138473a4433c853c6e66e7aabc237">◆ </a></span>controlledNot()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void controlledNot </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply the controlled not (single control, single target) gate, also known as the c-X, c-sigma-X, c-Pauli-X and c-bit-flip gate. </p>
<p>This applies pauliX to the target qubit if the control qubit has value 1. This effects the two-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & & 1 \\ & & 1 \end{pmatrix} \]" src="form_127.png"/>
</p>
<p> on the control and target qubits.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, -.5); \draw (-2,0) -- (2, 0); \draw (0, 0) circle (.5); \end{tikzpicture} \]" src="form_128.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gafd81a9217fb7d21c365443442492b2dc" title="Apply a NOT (or Pauli X) gate with multiple control and target qubits.">multiControlledMultiQubitNot()</a></li>
<li><a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>the state-vector or density matrix to modify </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>nots the target if this qubit is 1 </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to not </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside <b>[0, </b><code>qureg.numQubitsRepresented</code><b>)</b></li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00524">524</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  {</div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  </div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <a class="code" href="QuEST__internal_8h.html#abb2eab4af99adcc59be24f4c91c6f6ad">statevec_controlledNot</a>(qureg, controlQubit, targetQubit);</div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <a class="code" href="QuEST__internal_8h.html#abb2eab4af99adcc59be24f4c91c6f6ad">statevec_controlledNot</a>(qureg, controlQubit+shift, targetQubit+shift);</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  }</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  </div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  <a class="code" href="QuEST__qasm_8c.html#aa4c380db9eda18892d5a86825fa4b165">qasm_recordControlledGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa13c9487aed515148e7594e35eb8dcc55">GATE_SIGMA_X</a>, controlQubit, targetQubit);</div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00021">GATE_SIGMA_X</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00239">qasm_recordControlledGate()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01075">statevec_controlledNot()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00295">TEST_CASE()</a>.</p>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ga5e5fdaa7d3dd449b3e2c5d4a01bd015a">◆ </a></span>controlledPauliY()</h2>
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<td class="memname">void controlledPauliY </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply the controlled pauliY (single control, single target) gate, also known as the c-Y and c-sigma-Y gate. </p>
<p>This applies pauliY to the target qubit if the control qubit has value 1. This effects the two-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & & -i \\ & & i \end{pmatrix} \]" src="form_135.png"/>
</p>
<p> on the control and target qubits.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {Y}; \end{tikzpicture} \]" src="form_136.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>applies pauliY to the target if this qubit is 1 </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to not </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd>
<dd>
Ania Brown (debug) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00563">563</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  {</div>
<div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  </div>
<div class="line"><a name="l00566"></a><span class="lineno"> 566</span>  <a class="code" href="QuEST__internal_8h.html#a4e19ef93d01d7acea32ca646d623aedd">statevec_controlledPauliY</a>(qureg, controlQubit, targetQubit);</div>
<div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  <a class="code" href="QuEST__internal_8h.html#a4a2fa262d3f0dba372797b9bd35d9fa5">statevec_controlledPauliYConj</a>(qureg, controlQubit+shift, targetQubit+shift);</div>
<div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  }</div>
<div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  </div>
<div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  <a class="code" href="QuEST__qasm_8c.html#aa4c380db9eda18892d5a86825fa4b165">qasm_recordControlledGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725faa29b98cbb581abf5ec338a1763de7a1b">GATE_SIGMA_Y</a>, controlQubit, targetQubit);</div>
<div class="line"><a name="l00573"></a><span class="lineno"> 573</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00022">GATE_SIGMA_Y</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00239">qasm_recordControlledGate()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01192">statevec_controlledPauliY()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01225">statevec_controlledPauliYConj()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00341">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga2fa310101ecffd6aeba96f77b7d85f56">◆ </a></span>controlledPhaseFlip()</h2>
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<td class="memname">void controlledPhaseFlip </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>idQubit1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>idQubit2</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Apply the (two-qubit) controlled phase flip gate, also known as the controlled pauliZ gate. </p>
<p>For each state, if both input qubits have value one, multiply the amplitude of that state by -1. This applies the two-qubit unitary: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & 1 \\ & & & -1 \end{pmatrix} \]" src="form_73.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {idQubit1}; \node[draw=none] at (-3.5, 0) {idQubit2}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 0); \draw (-2,0) -- (2, 0); \draw[fill=black] (0, 0) circle (.2); \end{tikzpicture} \]" src="form_74.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga5d80b490e3910aa737a81bb597cdfcc9" title="Apply the single-qubit Pauli-Z (also known as the Z, sigma-Z or phase-flip) gate.">pauliZ()</a></li>
<li><a class="el" href="group__unitary.html#ga26baa057f5db8804825c2d611386753b" title="Shift the phase between and of a single qubit by a given angle.">phaseShift()</a></li>
<li><a class="el" href="group__unitary.html#gad76781842af56821ed4e223bd776f057" title="Apply the multiple-qubit controlled phase flip gate, also known as the multiple-qubit controlled paul...">multiControlledPhaseFlip()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">idQubit1,idQubit2</td><td>qubits to operate upon </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>idQubit1</code> or <code>idQubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>idQubit1</code> and <code>idQubit2</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00575">575</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  {</div>
<div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, idQubit1, idQubit2, __func__);</div>
<div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  </div>
<div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  <a class="code" href="QuEST__internal_8h.html#aaf78491e35d165edfd57387f9fffecbd">statevec_controlledPhaseFlip</a>(qureg, idQubit1, idQubit2);</div>
<div class="line"><a name="l00579"></a><span class="lineno"> 579</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  <a class="code" href="QuEST__internal_8h.html#aaf78491e35d165edfd57387f9fffecbd">statevec_controlledPhaseFlip</a>(qureg, idQubit1+shift, idQubit2+shift);</div>
<div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  }</div>
<div class="line"><a name="l00583"></a><span class="lineno"> 583</span>  </div>
<div class="line"><a name="l00584"></a><span class="lineno"> 584</span>  <a class="code" href="QuEST__qasm_8c.html#aa4c380db9eda18892d5a86825fa4b165">qasm_recordControlledGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa228cd6a7ad18928b794ee7ad1f1fc85e">GATE_SIGMA_Z</a>, idQubit1, idQubit2);</div>
<div class="line"><a name="l00585"></a><span class="lineno"> 585</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00023">GATE_SIGMA_Z</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00239">qasm_recordControlledGate()</a>, <a class="el" href="QuEST__cpu_8c_source.html#l03687">statevec_controlledPhaseFlip()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00387">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga7214a79aa22ae7a50ad6f38615968cb0">◆ </a></span>controlledPhaseShift()</h2>
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<td class="memname">void controlledPhaseShift </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>idQubit1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>idQubit2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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</div><div class="memdoc">
<p>Introduce a phase factor <img class="formulaInl" alt="$ \exp(i \theta) $" src="form_67.png"/> on state <img class="formulaInl" alt="$ |11\rangle $" src="form_68.png"/> of qubits <code>idQubit1</code> and <code>idQubit2</code>. </p>
<p>For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/>, this effects the unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 & & & \\ & 1 & & \\ & & 1 & \\ & & & \exp(i \theta) \end{pmatrix} \]" src="form_69.png"/>
</p>
<p> on <code>idQubit1</code> and <code>idQubit2</code>.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {qubit1}; \node[draw=none] at (-3.5, 0) {qubit2}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_\theta$}; \end{tikzpicture} \]" src="form_70.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga26baa057f5db8804825c2d611386753b" title="Shift the phase between and of a single qubit by a given angle.">phaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga0832e39058d913ad47af44e97a854446" title="Introduce a phase factor on state of the passed qubits.">multiControlledPhaseShift()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">idQubit1</td><td>first qubit in the state to phase shift </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">idQubit2</td><td>second qubit in the state to phase shift </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>amount by which to shift the phase in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>idQubit1</code> or <code>idQubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>idQubit1</code> and <code>idQubit2</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00498">498</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  {</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, idQubit1, idQubit2, __func__);</div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  </div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  <a class="code" href="QuEST__internal_8h.html#a63df1ec14ff7cc81c3f392ac10fcc744">statevec_controlledPhaseShift</a>(qureg, idQubit1, idQubit2, angle);</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <a class="code" href="QuEST__internal_8h.html#a63df1ec14ff7cc81c3f392ac10fcc744">statevec_controlledPhaseShift</a>(qureg, idQubit1+shift, idQubit2+shift, -angle);</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  }</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  </div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  <a class="code" href="QuEST__qasm_8c.html#ae776148507b8f769cd00d1603212a028">qasm_recordControlledParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa4668b36d21aaeba1fb605b73881ca507">GATE_PHASE_SHIFT</a>, idQubit1, idQubit2, angle);</div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00032">GATE_PHASE_SHIFT</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00248">qasm_recordControlledParamGate()</a>, <a class="el" href="QuEST__cpu_8c_source.html#l03226">statevec_controlledPhaseShift()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00433">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga0c84c429cb1d7e2596706c1804dd9cba"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga0c84c429cb1d7e2596706c1804dd9cba">◆ </a></span>controlledRotateAroundAxis()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void controlledRotateAroundAxis </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structVector.html">Vector</a> </td>
<td class="paramname"><em>axis</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Applies a controlled rotation by a given angle around a given vector on the Bloch-sphere. </p>
<p><br />
The vector must not be zero (else an error is thrown), but needn't be unit magnitude.</p>
<p>For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/> and axis vector <img class="formulaInl" alt="$\vec{n}$" src="form_101.png"/>, applies <img class="formulaInl" alt="$R_{\hat{n}} = \exp \left(- i \frac{\theta}{2} \hat{n} \cdot \vec{\sigma} \right) $" src="form_102.png"/> to states where the target qubit is 1 ( <img class="formulaInl" alt="$\vec{\sigma}$" src="form_103.png"/> is the vector of Pauli matrices).</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_{\hat{n}}(\theta)$}; \end{tikzpicture} \]" src="form_107.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145" title="Rotate a single qubit by a given angle around a given Vector on the Bloch-sphere.">rotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>qubit with value 1 in the rotated states </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate in radians </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">axis</td><td>vector around which to rotate (can be non-unit; will be normalised) </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal</li>
<li>if <code>axis</code> is the zero vector </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00614">614</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00614"></a><span class="lineno"> 614</span>  {</div>
<div class="line"><a name="l00615"></a><span class="lineno"> 615</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00616"></a><span class="lineno"> 616</span>  <a class="code" href="QuEST__validation_8c.html#a782c6f57939eeb72b7be8e247979f3be">validateVector</a>(axis, __func__);</div>
<div class="line"><a name="l00617"></a><span class="lineno"> 617</span>  </div>
<div class="line"><a name="l00618"></a><span class="lineno"> 618</span>  <a class="code" href="QuEST__common_8c.html#a336c3286d2434fc892ebe20e9fa22a24">statevec_controlledRotateAroundAxis</a>(qureg, controlQubit, targetQubit, angle, axis);</div>
<div class="line"><a name="l00619"></a><span class="lineno"> 619</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00620"></a><span class="lineno"> 620</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00621"></a><span class="lineno"> 621</span>  <a class="code" href="QuEST__common_8c.html#a5ea2384a9b33c94eac891aacbfa5da6a">statevec_controlledRotateAroundAxisConj</a>(qureg, controlQubit+shift, targetQubit+shift, angle, axis);</div>
<div class="line"><a name="l00622"></a><span class="lineno"> 622</span>  }</div>
<div class="line"><a name="l00623"></a><span class="lineno"> 623</span>  </div>
<div class="line"><a name="l00624"></a><span class="lineno"> 624</span>  <a class="code" href="QuEST__qasm_8c.html#a33be8162c9633bb8015f06b38cf70735">qasm_recordControlledAxisRotation</a>(qureg, angle, axis, controlQubit, targetQubit);</div>
<div class="line"><a name="l00625"></a><span class="lineno"> 625</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00301">qasm_recordControlledAxisRotation()</a>, <a class="el" href="QuEST__common_8c_source.html#l00330">statevec_controlledRotateAroundAxis()</a>, <a class="el" href="QuEST__common_8c_source.html#l00337">statevec_controlledRotateAroundAxisConj()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00511">validateVector()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00480">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga13f904b417f647c70d163770e65906fc"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga13f904b417f647c70d163770e65906fc">◆ </a></span>controlledRotateX()</h2>
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<td class="memname">void controlledRotateX </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Applies a controlled rotation by a given angle around the X-axis of the Bloch-sphere. </p>
<p>The target qubit is rotated in states where the control qubit has value 1.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_x(\theta)$}; \end{tikzpicture} \]" src="form_104.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#gafbbded98b7233f5da06d74d1db5cbfdb" title="Applies a controlled rotation by a given angle around the Y-axis of the Bloch-sphere.">controlledRotateY()</a></li>
<li><a class="el" href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120" title="Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere.">controlledRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga0c84c429cb1d7e2596706c1804dd9cba" title="Applies a controlled rotation by a given angle around a given vector on the Bloch-sphere.">controlledRotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0" title="Introduce a phase factor on state of qubits idQubit1 and idQubit2.">controlledPhaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>qubit which has value 1 in the rotated states </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate the target qubit in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00220">220</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  {</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  </div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <a class="code" href="QuEST__common_8c.html#aa32eed5bc38e85193e1aa23b74e8541b">statevec_controlledRotateX</a>(qureg, controlQubit, targetQubit, angle);</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <a class="code" href="QuEST__common_8c.html#aa32eed5bc38e85193e1aa23b74e8541b">statevec_controlledRotateX</a>(qureg, controlQubit+shift, targetQubit+shift, -angle);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  }</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <a class="code" href="QuEST__qasm_8c.html#ae776148507b8f769cd00d1603212a028">qasm_recordControlledParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fada07505b73935b2788032efd30a1a361">GATE_ROTATE_X</a>, controlQubit, targetQubit, angle);</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00027">GATE_ROTATE_X</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00248">qasm_recordControlledParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00346">statevec_controlledRotateX()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00542">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gafbbded98b7233f5da06d74d1db5cbfdb"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gafbbded98b7233f5da06d74d1db5cbfdb">◆ </a></span>controlledRotateY()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void controlledRotateY </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Applies a controlled rotation by a given angle around the Y-axis of the Bloch-sphere. </p>
<p>The target qubit is rotated in states where the control qubit has value 1.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_y(\theta)$}; \end{tikzpicture} \]" src="form_105.png"/>
</p>
<ul>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#ga13f904b417f647c70d163770e65906fc" title="Applies a controlled rotation by a given angle around the X-axis of the Bloch-sphere.">controlledRotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120" title="Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere.">controlledRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga0c84c429cb1d7e2596706c1804dd9cba" title="Applies a controlled rotation by a given angle around a given vector on the Bloch-sphere.">controlledRotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0" title="Introduce a phase factor on state of qubits idQubit1 and idQubit2.">controlledPhaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>qubit which has value 1 in the rotated states </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate the target qubit in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00232">232</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  {</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  </div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <a class="code" href="QuEST__common_8c.html#ade67874c89179541f616b3685595d3ae">statevec_controlledRotateY</a>(qureg, controlQubit, targetQubit, angle);</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <a class="code" href="QuEST__common_8c.html#ade67874c89179541f616b3685595d3ae">statevec_controlledRotateY</a>(qureg, controlQubit+shift, targetQubit+shift, angle); <span class="comment">// rotateY is real</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  }</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  </div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <a class="code" href="QuEST__qasm_8c.html#ae776148507b8f769cd00d1603212a028">qasm_recordControlledParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fae1267d5de573dc2901aa8e724ac1d689">GATE_ROTATE_Y</a>, controlQubit, targetQubit, angle);</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00028">GATE_ROTATE_Y</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00248">qasm_recordControlledParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00352">statevec_controlledRotateY()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00591">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga7eb969c1dd6c949aecf716d2fba71120"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga7eb969c1dd6c949aecf716d2fba71120">◆ </a></span>controlledRotateZ()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void controlledRotateZ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere. </p>
<p>The target qubit is rotated in states where the control qubit has value 1.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_z(\theta)$}; \end{tikzpicture} \]" src="form_106.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga13f904b417f647c70d163770e65906fc" title="Applies a controlled rotation by a given angle around the X-axis of the Bloch-sphere.">controlledRotateX()</a></li>
<li><a class="el" href="group__unitary.html#gafbbded98b7233f5da06d74d1db5cbfdb" title="Applies a controlled rotation by a given angle around the Y-axis of the Bloch-sphere.">controlledRotateY()</a></li>
<li><a class="el" href="group__unitary.html#ga0c84c429cb1d7e2596706c1804dd9cba" title="Applies a controlled rotation by a given angle around a given vector on the Bloch-sphere.">controlledRotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0" title="Introduce a phase factor on state of qubits idQubit1 and idQubit2.">controlledPhaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>qubit which has value 1 in the rotated states </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate the target qubit in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00244">244</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  {</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  </div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <a class="code" href="QuEST__common_8c.html#a3e11a9b9fa5ee16d4738a97f4590ee61">statevec_controlledRotateZ</a>(qureg, controlQubit, targetQubit, angle);</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <a class="code" href="QuEST__common_8c.html#a3e11a9b9fa5ee16d4738a97f4590ee61">statevec_controlledRotateZ</a>(qureg, controlQubit+shift, targetQubit+shift, -angle);</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  }</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  </div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <a class="code" href="QuEST__qasm_8c.html#ae776148507b8f769cd00d1603212a028">qasm_recordControlledParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa0cdc4c588d02a515a68515dd3f24d877">GATE_ROTATE_Z</a>, controlQubit, targetQubit, angle);</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00029">GATE_ROTATE_Z</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00248">qasm_recordControlledParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00358">statevec_controlledRotateZ()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00638">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga3d89916b46bc4aaf23e938022e6c89c1"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga3d89916b46bc4aaf23e938022e6c89c1">◆ </a></span>controlledTwoQubitUnitary()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void controlledTwoQubitUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix4.html">ComplexMatrix4</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a general controlled two-qubit unitary (including a global phase factor). </p>
<p>The given unitary is applied to the target amplitudes where the control qubit has value 1. This effects the many-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\ & & 1 \\ & & & 1 \\ & & & & u_{00} & u_{01} & u_{02} & u_{03} \\ & & & & u_{10} & u_{11} & u_{12} & u_{13} \\ & & & & u_{20} & u_{21} & u_{22} & u_{23} \\ & & & & u_{30} & u_{31} & u_{32} & u_{33} \end{pmatrix} \]" src="form_213.png"/>
</p>
<p> on the control and target qubits.</p>
<p><code>targetQubit1</code> is treated as the <code>least</code> significant qubit in <code>u</code>, such that a row in <code>u</code> is dotted with the vector <img class="formulaInl" alt="$ |\text{targetQubit2} \;\; \text{targetQubit1}\rangle : \{ |00\rangle, |01\rangle, |10\rangle, |11\rangle \} $" src="form_211.png"/></p>
<p>The passed 4x4 ComplexMatrix must be unitary, otherwise an error is thrown.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target1}; \node[draw=none] at (-3.5, 2) {target2}; \node[draw=none] at (-3.5, 4) {control}; \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, 3); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-2,2) -- (-1, 2); \draw (1, 2) -- (2, 2); \draw (-1,-1)--(-1,3)--(1,3)--(1,-1)--cycle; \node[draw=none] at (0, 1) {U}; \end{tikzpicture} \]" src="form_214.png"/>
</p>
<p>Note that in distributed mode, this routine requires that each node contains at least 4 amplitudes. This means an q-qubit register (state vector or density matrix) can be distributed by at most 2^q/4 nodes.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix4.html" title="Represents a 4x4 matrix of complex numbers.">ComplexMatrix4</a></li>
<li><a class="el" href="group__unitary.html#ga65c7879947e398690a5428bd43e143e3" title="Apply a general multi-controlled two-qubit unitary (including a global phase factor).">multiControlledTwoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
</ul>
</dd></dl>
<p><br />
</p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>the control qubit which must be in state 1 to effect the given unitary </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit1</td><td>first qubit to operate on, treated as least significant in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit2</td><td>second qubit to operate on, treated as most significant in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>controlQubit</code>, <code>targetQubit1</code> or <code>targetQubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if any of <code>controlQubit</code>, <code>targetQubit1</code> and <code>targetQubit2</code> are equal</li>
<li>if matrix <code>u</code> is not unitary<ul>
<li>if each node cannot fit 4 amplitudes in distributed mode. </li>
</ul>
</li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00269">269</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  {</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, (<span class="keywordtype">int</span>[]) {controlQubit}, 1, (<span class="keywordtype">int</span>[]) {targetQubit1, targetQubit2}, 2, __func__);</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  <a class="code" href="QuEST__validation_8c.html#a654db9d60abdcae26427e7d3b3d9c432">validateTwoQubitUnitaryMatrix</a>(qureg, u, __func__);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <a class="code" href="QuEST__common_8c.html#ad7ac4934371d72e24c6d1cea3d3da391">statevec_controlledTwoQubitUnitary</a>(qureg, controlQubit, targetQubit1, targetQubit2, u);</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <a class="code" href="QuEST__common_8c.html#ad7ac4934371d72e24c6d1cea3d3da391">statevec_controlledTwoQubitUnitary</a>(qureg, controlQubit+shift, targetQubit1+shift, targetQubit2+shift, <a class="code" href="QuEST__common_8c.html#a20d45e85dd49dd3bf6045990b590b24b">getConjugateMatrix4</a>(u));</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  }</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  </div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, <span class="stringliteral">"Here, an undisclosed controlled 2-qubit unitary was applied."</span>);</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00110">getConjugateMatrix4()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00567">statevec_controlledTwoQubitUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00481">validateTwoQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00685">TEST_CASE()</a>.</p>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gaa3fb996a5cadd098f4acd8aec955cf9c">◆ </a></span>controlledUnitary()</h2>
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<td class="memname">void controlledUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>controlQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply a general controlled unitary (single control, single target), which can include a global phase factor. </p>
<p>The given unitary is applied to the target qubit if the control qubit has value 1, effecting the two-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\ & & u_{00} & u_{01}\\ & & u_{10} & u_{11} \end{pmatrix} \]" src="form_110.png"/>
</p>
<p> on the control and target qubits.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {control}; \node[draw=none] at (-3.5, 0) {target}; \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {U}; \end{tikzpicture} \]" src="form_111.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix2.html" title="Represents a 2x2 matrix of complex numbers.">ComplexMatrix2</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332" title="Apply a general multiple-control single-target unitary, which can include a global phase factor.">multiControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga41b946a82982c3fa3dc2a7395665bc90" title="Apply a general single-qubit unitary with multiple control qubits, conditioned upon a specific bit se...">multiStateControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
</ul>
</dd></dl>
<p><br />
</p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubit</td><td>apply unitary if this qubit is 1 </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>single-qubit unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>controlQubit</code> or <code>targetQubit</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubit</code> and <code>targetQubit</code> are equal</li>
<li>if <code>u</code> is not unitary </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00360">360</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  {</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <a class="code" href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a>(qureg, controlQubit, targetQubit, __func__);</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <a class="code" href="QuEST__validation_8c.html#a0344fbbb2bb505f7db14b420153f1eb5">validateOneQubitUnitaryMatrix</a>(u, __func__);</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  </div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <a class="code" href="QuEST__internal_8h.html#add9ca9956cdd81ed5d0b0f66168c04a3">statevec_controlledUnitary</a>(qureg, controlQubit, targetQubit, u);</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <a class="code" href="QuEST__internal_8h.html#add9ca9956cdd81ed5d0b0f66168c04a3">statevec_controlledUnitary</a>(qureg, controlQubit+shift, targetQubit+shift, <a class="code" href="QuEST__common_8c.html#ad34d98eeaa6a3cb45e92c696cfd2d1c8">getConjugateMatrix2</a>(u));</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  }</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  </div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  <a class="code" href="QuEST__qasm_8c.html#a5e99d405002cdf6ddd40922911d058a4">qasm_recordControlledUnitary</a>(qureg, u, controlQubit, targetQubit);</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00105">getConjugateMatrix2()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00279">qasm_recordControlledUnitary()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l00972">statevec_controlledUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00408">validateControlTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00477">validateOneQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00762">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga6532decd6c404189915563492f090e6f">◆ </a></span>hadamard()</h2>
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<td class="memname">void hadamard </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply the single-qubit Hadamard gate. </p>
<p>This takes <img class="formulaInl" alt="$|0\rangle$" src="form_121.png"/> to <img class="formulaInl" alt="$|+\rangle$" src="form_122.png"/> and <img class="formulaInl" alt="$|1\rangle$" src="form_123.png"/> to <img class="formulaInl" alt="$|-\rangle$" src="form_124.png"/>, and is equivalent to a rotation of <img class="formulaInl" alt="$\pi$" src="form_114.png"/> around the x-axis then <img class="formulaInl" alt="$\pi/2$" src="form_77.png"/> about the y-axis on the Bloch-sphere. I.e. </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix} \]" src="form_125.png"/>
</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {H}; \end{tikzpicture} \]" src="form_126.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00176">176</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  {</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  </div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <a class="code" href="QuEST__internal_8h.html#af3fc7bd149c70f083b149050242cd55e">statevec_hadamard</a>(qureg, targetQubit);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <a class="code" href="QuEST__internal_8h.html#af3fc7bd149c70f083b149050242cd55e">statevec_hadamard</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  }</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  </div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <a class="code" href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa8417e56d80add49216437e0d451e8dd9">GATE_HADAMARD</a>, targetQubit);</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00026">GATE_HADAMARD</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00179">qasm_recordGate()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01258">statevec_hadamard()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00814">TEST_CASE()</a>.</p>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gafd81a9217fb7d21c365443442492b2dc">◆ </a></span>multiControlledMultiQubitNot()</h2>
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<td class="memname">void multiControlledMultiQubitNot </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>ctrls</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numCtrls</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargs</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a NOT (or Pauli X) gate with multiple control and target qubits. </p>
<p>This applies pauliX to qubits <code>targs</code> on every basis state for which the control qubits <code>ctrls</code> are all in the <img class="formulaInl" alt="$|1\rangle$" src="form_123.png"/> state. The ordering within each of <code>ctrls</code> and <code>targs</code> has no effect on the operation. </p><blockquote class="doxtable">
<p>This function is equivalent, but significantly faster (approximately <code>numTargs</code> times) than applying controlled NOTs on each qubit in <code>targs</code> in turn, since: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ C_{a, \,b, \,\dots}( X_c \otimes X_d \otimes \dots ) \equiv C_{a, \,b, \,\dots}( X_c) \; \otimes \; C_{a, \,b, \,\dots}(X_d) \; \otimes \; \dots \]" src="form_129.png"/>
</p>
</blockquote>
<p>The effected unitary, if <code>targs</code> and <code>ctrls</code> happened to be contiguous, has matrix: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & \ddots \\ & & & & & & {{\scriptstyle\cdot}^{{\scriptstyle\cdot}^{{\scriptstyle\cdot}}}} \\ & & & & & 1 & \\ & & & & 1 & & \\ & & & {{\scriptstyle\cdot}^{{\scriptstyle\cdot}^{{\scriptstyle\cdot}}}} & & & \end{pmatrix} \]" src="form_130.png"/>
</p>
<p> and circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 1) {targets}; \node[draw=none] at (-3.5, 5) {controls}; \node[draw=none] at (0, 8) {$\vdots$}; \draw (0, 7) -- (0, 6); \draw (-2, 6) -- (2, 6); \draw[fill=black] (0, 6) circle (.2); \draw (0, 6) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, -1); \draw (-2,2) -- (2, 2); \draw (0, 2) circle (.4); \draw (-2,0) -- (2, 0); \draw (0, 0) circle (.4); \node[draw=none] at (0, -1.5) {$\vdots$}; \end{tikzpicture} \]" src="form_131.png"/>
</p>
<blockquote class="doxtable">
<p>In distributed mode, this operation requires at most a single round of pair-wise communication between nodes, and hence is as efficient as <a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a>. </p>
</blockquote>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga7e58e8131f219f48e5b7410ca8dfe0c0" title="Apply a NOT (or Pauli X) gate with multiple target qubits, which has the same effect as (but is much ...">multiQubitNot()</a></li>
<li><a class="el" href="group__unitary.html#gaa5a138473a4433c853c6e66e7aabc237" title="Apply the controlled not (single control, single target) gate, also known as the c-X,...">controlledNot()</a></li>
<li><a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>a state-vector or density matrix to modify </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">ctrls</td><td>a list of the control qubit indices </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numCtrls</td><td>the length of list <code>ctrls</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targs</td><td>a list of the qubits to be targeted by the X gates </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargs</td><td>the length of list <code>targs</code> </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if any qubit in <code>ctrls</code> and <code>targs</code> is invalid, i.e. outside <b>[0, </b><code>qureg.numQubitsRepresented</code><b>)</b></li>
<li>if <code>ctrls</code> or <code>targs</code> contain any repetitions</li>
<li>if any qubit in <code>ctrls</code> is also in <code>targs</code> (and vice versa)</li>
<li>if <code>numTargs</code> <b>< 1</b></li>
<li>if <code>numCtrls</code> <b>< 1</b> (use <a class="el" href="group__unitary.html#ga7e58e8131f219f48e5b7410ca8dfe0c0" title="Apply a NOT (or Pauli X) gate with multiple target qubits, which has the same effect as (but is much ...">multiQubitNot()</a> for no controls) </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>ctrls</code> contains fewer elements than <code>numCtrls</code> </li>
<li>if <code>targs</code> contains fewer elements than <code>numTargs</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00549">549</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  {</div>
<div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, ctrls, numCtrls, targs, numTargs, __func__);</div>
<div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  </div>
<div class="line"><a name="l00552"></a><span class="lineno"> 552</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(ctrls, numCtrls);</div>
<div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> targMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(targs, numTargs);</div>
<div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <a class="code" href="QuEST__internal_8h.html#a13ecc24b355a5213d745651cde56bd71">statevec_multiControlledMultiQubitNot</a>(qureg, ctrlMask, targMask);</div>
<div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <a class="code" href="QuEST__internal_8h.html#a13ecc24b355a5213d745651cde56bd71">statevec_multiControlledMultiQubitNot</a>(qureg, ctrlMask<<shift, targMask<<shift);</div>
<div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  }</div>
<div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  </div>
<div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <a class="code" href="QuEST__qasm_8c.html#a2275a3f14e8853261533ee41416ae19d">qasm_recordMultiControlledMultiQubitNot</a>(qureg, ctrls, numCtrls, targs, numTargs);</div>
<div class="line"><a name="l00561"></a><span class="lineno"> 561</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00382">qasm_recordMultiControlledMultiQubitNot()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01097">statevec_multiControlledMultiQubitNot()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00854">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga3ad6c477edcdbc845fc1143e860fda08"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga3ad6c477edcdbc845fc1143e860fda08">◆ </a></span>multiControlledMultiQubitUnitary()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">void multiControlledMultiQubitUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>ctrls</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numCtrls</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrixN.html">ComplexMatrixN</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a general multi-controlled multi-qubit unitary (including a global phase factor). </p>
<p>Any number of control and target qubits can be specified. This effects the many-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & \ddots \\ & & & u_{00} & u_{01} & \dots \\ & & & u_{10} & u_{11} & \dots \\ & & & \vdots & \vdots & \ddots \end{pmatrix} \]" src="form_221.png"/>
</p>
<p> on the control and target qubits.</p>
<p>The target qubits in <code>targs</code> are treated as ordered least significant to most significant in <code>u</code>.</p>
<p>The passed <a class="el" href="structComplexMatrixN.html" title="Represents a general 2^N by 2^N matrix of complex numbers.">ComplexMatrixN</a> must be unitary and be a compatible size with the specified number of target qubits, otherwise an error is thrown. </p><blockquote class="doxtable">
<p>To left-multiply a non-unitary <a class="el" href="structComplexMatrixN.html" title="Represents a general 2^N by 2^N matrix of complex numbers.">ComplexMatrixN</a>, including control qubits, use <a class="el" href="group__operator.html#gab52b6315c5520b7d311b0458785eed8e" title="Apply a general N-by-N matrix, which may be non-unitary, with additional controlled qubits.">applyMultiControlledMatrixN()</a> </p>
</blockquote>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 1) {targets}; \node[draw=none] at (-3.5, 5) {controls}; \node[draw=none] at (0, 8) {$\vdots$}; \draw (0, 7) -- (0, 6); \draw (-2, 6) -- (2, 6); \draw[fill=black] (0, 6) circle (.2); \draw (0, 6) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, 3); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-2,2) -- (-1, 2); \draw (1, 2) -- (2, 2); \draw (-1,-1)--(-1,3)--(1,3)--(1,-1); \node[draw=none] at (0, 1) {U}; \node[draw=none] at (0, -1) {$\vdots$}; \end{tikzpicture} \]" src="form_222.png"/>
</p>
<p>Note that in multithreaded mode, each thread will clone 2^<code>numTargs</code> amplitudes, and store these in the runtime stack. Using t threads, the total memory overhead of this function is t*2^<code>numTargs</code>. For many targets (e.g. 16 qubits), this may cause a stack-overflow / seg-fault (e.g. on a 1 MiB stack).</p>
<p>Note that in distributed mode, this routine requires that each node contains at least 2^<code>numTargs</code> amplitudes. This means an q-qubit register (state vector or density matrix) can be distributed by at most 2^q / 2^<code>numTargs</code> nodes.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__type.html#ga815103261fb22ea9690e1427571df00e" title="Allocate dynamic memory for a square complex matrix of any size, which can be passed to functions lik...">createComplexMatrixN()</a></li>
<li><a class="el" href="group__operator.html#gab52b6315c5520b7d311b0458785eed8e" title="Apply a general N-by-N matrix, which may be non-unitary, with additional controlled qubits.">applyMultiControlledMatrixN()</a></li>
<li><a class="el" href="group__unitary.html#gafd81a9217fb7d21c365443442492b2dc" title="Apply a NOT (or Pauli X) gate with multiple control and target qubits.">multiControlledMultiQubitNot()</a></li>
<li><a class="el" href="group__unitary.html#gaeb975903209000ebbaf50ef1cc353a79" title="Apply a general controlled multi-qubit unitary (including a global phase factor).">controlledMultiQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">ctrls</td><td>a list of the control qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numCtrls</td><td>the number of control qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targs</td><td>a list of the target qubits, ordered least to most significant </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargs</td><td>the number of target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if any qubit in <code>ctrls</code> and <code>targs</code> is invalid, i.e. outside <b>[0, </b><code>qureg.numQubitsRepresented</code><b>)</b></li>
<li>if <code>ctrls</code> or <code>targs</code> contain any repetitions</li>
<li>if any qubit in <code>ctrls</code> is also in <code>targs</code> (and vice versa)</li>
<li>if <code>numTargs</code> <b>< 1</b></li>
<li>if <code>numCtrls</code> <b>< 1</b> (use <a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a> for no controls)</li>
<li>if matrix <code>u</code> is not unitary</li>
<li>if a node cannot fit the required number of target amplitudes in distributed mode </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>ctrls</code> contains fewer elements than <code>numCtrls</code> </li>
<li>if <code>targs</code> contains fewer elements than <code>numTargs</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00330">330</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  {</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, ctrls, numCtrls, targs, numTargs, __func__);</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <a class="code" href="QuEST__validation_8c.html#ab9947ff071a0c019f715f04b3833dcfd">validateMultiQubitUnitaryMatrix</a>(qureg, u, numTargs, __func__);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  </div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(ctrls, numCtrls);</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <a class="code" href="QuEST__internal_8h.html#a0acfe30083d0bc2a84da196378a36122">statevec_multiControlledMultiQubitUnitary</a>(qureg, ctrlMask, targs, numTargs, u);</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targs, numTargs, shift);</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <a class="code" href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a>(u);</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <a class="code" href="QuEST__internal_8h.html#a0acfe30083d0bc2a84da196378a36122">statevec_multiControlledMultiQubitUnitary</a>(qureg, ctrlMask<<shift, targs, numTargs, u);</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targs, numTargs, -shift);</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <a class="code" href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a>(u);</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  }</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  </div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, <span class="stringliteral">"Here, an undisclosed multi-controlled multi-qubit unitary was applied."</span>);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00115">setConjugateMatrixN()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01514">statevec_multiControlledMultiQubitUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00502">validateMultiQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l00950">TEST_CASE()</a>.</p>
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<a id="gab2ececaa253252e1b1cdb18a8452704a"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gab2ececaa253252e1b1cdb18a8452704a">◆ </a></span>multiControlledMultiRotatePauli()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void multiControlledMultiRotatePauli </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControls</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targetQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">enum <a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028">pauliOpType</a> * </td>
<td class="paramname"><em>targetPaulis</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargets</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a multi-controlled multi-target multi-Pauli rotation, also known as a controlled Pauli gadget. </p>
<p>This is the unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ |1\rangle\langle 1|^{\otimes\, \text{numControls}} \; \otimes \, \exp \left( - i \, \frac{\theta}{2} \; \bigotimes_{j}^{\text{numTargets}} \hat{\sigma}_j\right) \;\;+\;\; \sum\limits_{k=0}^{2^{\,\text{numControls}} - 2} |k\rangle\langle k| \otimes \text{I} \]" src="form_191.png"/>
</p>
<p> where <img class="formulaInl" alt="$\hat{\sigma}_j$" src="form_192.png"/> are the Pauli operators (<a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028" title="Codes for specifying Pauli operators.">pauliOpType</a>) in <code>targetPaulis</code>, which operate upon the corresponding qubits in <code>targetQubits</code>.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-4, 1) {targets}; \node[draw=none] at (-4, 5) {controls}; \node[draw=none] at (0, 8) {$\vdots$}; \draw (0, 7) -- (0, 6); \draw (-2.5, 6) -- (2.5, 6); \draw[fill=black] (0, 6) circle (.2); \draw (0, 6) -- (0, 4); \draw (-2.5, 4) -- (2.5, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, 3); \draw (-2.5,0) -- (-1.5, 0); \draw (1.5, 0) -- (2.5, 0); \draw (-2.5,2) -- (-1.5, 2); \draw (1.5, 2) -- (2.5, 2); \draw (-1.5,-1)--(-1.5,3)--(1.5,3)--(1.5,-1); \node[draw=none] at (0, 1) {$e^{-i\frac{\theta}{2} \bigotimes\limits_j \hat{\sigma}_j }$}; \node[draw=none] at (0, -1) {$\vdots$}; \end{tikzpicture} \]" src="form_193.png"/>
</p>
<blockquote class="doxtable">
<p>All qubits not appearing in <code>targetQubits</code> and <code>controlQubits</code> are assumed to receive the identity operator. </p>
</blockquote>
<p>For example: </p><div class="fragment"><div class="line"><span class="keywordtype">int</span> numCtrls = 1;</div>
<div class="line"><span class="keywordtype">int</span> numTargs = 4;</div>
<div class="line"><span class="keywordtype">int</span> ctrls[] = {4};</div>
<div class="line"><span class="keywordtype">int</span> targs[] = {0,1,2,3};</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028">pauliOpType</a> paulis[] = {<a class="code" href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a7abac7bb5b71e17382014c443244ad5c">PAULI_X</a>, <a class="code" href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a2c64a9aaee27f6bcfef894d159e759bd">PAULI_Y</a>, <a class="code" href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a085c85cff6ba79c52d8b1e61c42ddddf">PAULI_Z</a>, <a class="code" href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a63800f45b01ccc2608f754aee850bf4a">PAULI_I</a>};</div>
<div class="line"> </div>
<div class="line"><a class="code" href="group__unitary.html#gab2ececaa253252e1b1cdb18a8452704a">multiControlledMultiRotatePauli</a>(</div>
<div class="line"> qureg, ctrls, numCtrls, targs, paulis, numTargs, 0.1);</div>
</div><!-- fragment --><p>effects </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ |1\rangle\langle 1 | \otimes \exp\left( -i \, (0.1/2) \, X_0 \, Y_1 \, Z_2 \right) \, \text{I}_3 \;\; + \;\; |0\rangle\langle 0| \otimes \text{I}^{\otimes 4} \]" src="form_194.png"/>
</p>
<p> on <code>qureg</code>, where unspecified qubits (along with those targeted by <code>PAULI_I</code>) are assumed to receive the identity operator (excluded from exponentiation).</p>
<blockquote class="doxtable">
<p>This means specifying <code>PAULI_I</code> does <em>not</em> induce a global phase factor <img class="formulaInl" alt="$\exp(-i \theta/2)$" src="form_188.png"/>. Hence, if all <code>targetPaulis</code> are identity, then this function does nothing to <code>qureg</code>. Specifying <code>PAULI_I</code> on a qubit is superfluous but allowed for convenience. </p>
</blockquote>
<p>This function effects the controlled Pauli gadget by first (controlled) rotating the qubits which are targeted with either <code>X</code> or <code>Y</code> into alternate basis, performing <a class="el" href="group__unitary.html#ga1e5dd165b402e97abaa0b807026527f2" title="Apply a multi-controlled multi-target Z rotation, also known as a controlled phase gadget.">multiControlledMultiRotateZ()</a> on all target qubits, then restoring the original basis.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga1e5dd165b402e97abaa0b807026527f2" title="Apply a multi-controlled multi-target Z rotation, also known as a controlled phase gadget.">multiControlledMultiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145" title="Rotate a single qubit by a given angle around a given Vector on the Bloch-sphere.">rotateAroundAxis()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>list of the indices of qubits to control upon </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControls</td><td>length of length <code>controlQubits</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubits</td><td>a list of the indices of the target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetPaulis</td><td>a list of the Pauli operators around which to rotate the target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargets</td><td>length of list <code>targetQubits</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>the angle by which the multi-qubit state is rotated around the Z axis </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if any qubit in <code>controlQubits</code> and <code>targetQubits</code> is invalid, i.e. outside <b>[0, </b><code>qureg.numQubitsRepresented</code><b>)</b></li>
<li>if <code>controlQubits</code> or <code>targetQubits</code> contain any repetitions</li>
<li>if any qubit in <code>controlQubits</code> is also in <code>targetQubits</code> (and vice versa)</li>
<li>if <code>numTargets</code> <b>< 1</b></li>
<li>if <code>numControls</code> <b>< 1</b> (use <a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a> for no controls)</li>
<li>if any element of <code>targetPaulis</code> is not one of <code>PAULI_I</code>, <code>PAULI_X</code>, <code>PAULI_Y</code>, <code>PAULI_Z</code> </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>controlQubits</code> contains fewer elements than <code>numControls</code> </li>
<li>if <code>targetQubits</code> contains fewer elements than <code>numTargets</code> </li>
<li>if <code>targetPaulis</code> contains fewer elements than <code>numTargets</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00705">705</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00705"></a><span class="lineno"> 705</span>  {</div>
<div class="line"><a name="l00706"></a><span class="lineno"> 706</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, controlQubits, numControls, targetQubits, numTargets, __func__);</div>
<div class="line"><a name="l00707"></a><span class="lineno"> 707</span>  <a class="code" href="QuEST__validation_8c.html#aa194ba5f5c6e19c6caa4c715b3dbefcc">validatePauliCodes</a>(targetPaulis, numTargets, __func__);</div>
<div class="line"><a name="l00708"></a><span class="lineno"> 708</span>  </div>
<div class="line"><a name="l00709"></a><span class="lineno"> 709</span>  <span class="keywordtype">int</span> conj=0;</div>
<div class="line"><a name="l00710"></a><span class="lineno"> 710</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(controlQubits, numControls);</div>
<div class="line"><a name="l00711"></a><span class="lineno"> 711</span>  <a class="code" href="QuEST__common_8c.html#a08d2e22870f3ef0289e355d634ea17a2">statevec_multiControlledMultiRotatePauli</a>(qureg, ctrlMask, targetQubits, targetPaulis, numTargets, angle, conj);</div>
<div class="line"><a name="l00712"></a><span class="lineno"> 712</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00713"></a><span class="lineno"> 713</span>  conj = 1;</div>
<div class="line"><a name="l00714"></a><span class="lineno"> 714</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00715"></a><span class="lineno"> 715</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targetQubits, numTargets, shift);</div>
<div class="line"><a name="l00716"></a><span class="lineno"> 716</span>  <a class="code" href="QuEST__common_8c.html#a08d2e22870f3ef0289e355d634ea17a2">statevec_multiControlledMultiRotatePauli</a>(qureg, ctrlMask<<shift, targetQubits, targetPaulis, numTargets, angle, conj);</div>
<div class="line"><a name="l00717"></a><span class="lineno"> 717</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targetQubits, numTargets, -shift);</div>
<div class="line"><a name="l00718"></a><span class="lineno"> 718</span>  }</div>
<div class="line"><a name="l00719"></a><span class="lineno"> 719</span>  </div>
<div class="line"><a name="l00720"></a><span class="lineno"> 720</span>  <span class="comment">// @TODO: create actual QASM</span></div>
<div class="line"><a name="l00721"></a><span class="lineno"> 721</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, </div>
<div class="line"><a name="l00722"></a><span class="lineno"> 722</span>  <span class="stringliteral">"Here a %d-control %d-target multiControlledMultiRotatePauli of angle %g was performed (QASM not yet implemented)"</span>,</div>
<div class="line"><a name="l00723"></a><span class="lineno"> 723</span>  numControls, numTargets, angle);</div>
<div class="line"><a name="l00724"></a><span class="lineno"> 724</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__common_8c_source.html#l00453">statevec_multiControlledMultiRotatePauli()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00599">validatePauliCodes()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01122">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga1e5dd165b402e97abaa0b807026527f2"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga1e5dd165b402e97abaa0b807026527f2">◆ </a></span>multiControlledMultiRotateZ()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void multiControlledMultiRotateZ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControls</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targetQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargets</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a multi-controlled multi-target Z rotation, also known as a controlled phase gadget. </p>
<p>This is the unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ |1\rangle\langle 1|^{\otimes\, \text{numControls}} \; \otimes \, \exp \left( - i \, \frac{\theta}{2} \; \bigotimes_{j}^{\text{numTargets}} Z_j\right) \;\;+\;\; \sum\limits_{k=0}^{2^{\,\text{numControls}} - 2} |k\rangle\langle k| \otimes \text{I} \]" src="form_189.png"/>
</p>
<p> where the Pauli Z gates operate upon the qubits in <code>targetQubits</code>, and cause rotations of <img class="formulaInl" alt="$\theta =$" src="form_182.png"/> <code>angle</code>.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-4, 1) {targets}; \node[draw=none] at (-4, 5) {controls}; \node[draw=none] at (0, 8) {$\vdots$}; \draw (0, 7) -- (0, 6); \draw (-2.5, 6) -- (2.5, 6); \draw[fill=black] (0, 6) circle (.2); \draw (0, 6) -- (0, 4); \draw (-2.5, 4) -- (2.5, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, 3); \draw (-2.5,0) -- (-1.5, 0); \draw (1.5, 0) -- (2.5, 0); \draw (-2.5,2) -- (-1.5, 2); \draw (1.5, 2) -- (2.5, 2); \draw (-1.5,-1)--(-1.5,3)--(1.5,3)--(1.5,-1); \node[draw=none] at (0, 1) {$e^{-i\frac{\theta}{2}Z^{\otimes}}$}; \node[draw=none] at (0, -1) {$\vdots$}; \end{tikzpicture} \]" src="form_190.png"/>
</p>
<blockquote class="doxtable">
<p>All qubits not appearing in <code>targetQubits</code> and <code>controlQubits</code> are assumed to receive the identity operator. </p>
</blockquote>
<p>This has the effect of premultiplying all amplitudes (for which the control qubits are <code>1</code>) with <img class="formulaInl" alt="$\exp(\pm i \theta/2)$" src="form_183.png"/>, where the sign is determined by the parity of the target qubits for that amplitude.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gab2ececaa253252e1b1cdb18a8452704a" title="Apply a multi-controlled multi-target multi-Pauli rotation, also known as a controlled Pauli gadget.">multiControlledMultiRotatePauli()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120" title="Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere.">controlledRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>list of the indices of qubits to control upon </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControls</td><td>length of length <code>controlQubits</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubits</td><td>a list of the indices of the target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargets</td><td>length of list <code>targetQubits</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>the angle by which the multi-qubit state is rotated around the Z axis </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if any qubit in <code>controlQubits</code> and <code>targetQubits</code> is invalid, i.e. outside <b>[0, </b><code>qureg.numQubitsRepresented</code><b>)</b></li>
<li>if <code>controlQubits</code> or <code>targetQubits</code> contain any repetitions</li>
<li>if any qubit in <code>controlQubits</code> is also in <code>targetQubits</code> (and vice versa)</li>
<li>if <code>numTargets</code> <b>< 1</b></li>
<li>if <code>numControls</code> <b>< 1</b> (use <a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a> for no controls) </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>controlQubits</code> contains fewer elements than <code>numControls</code> </li>
<li>if <code>targetQubits</code> contains fewer elements than <code>numTargets</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00668">668</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00668"></a><span class="lineno"> 668</span>  {</div>
<div class="line"><a name="l00669"></a><span class="lineno"> 669</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, controlQubits, numControls, targetQubits, numTargets, __func__);</div>
<div class="line"><a name="l00670"></a><span class="lineno"> 670</span>  </div>
<div class="line"><a name="l00671"></a><span class="lineno"> 671</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(controlQubits, numControls);</div>
<div class="line"><a name="l00672"></a><span class="lineno"> 672</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> targMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(targetQubits, numTargets);</div>
<div class="line"><a name="l00673"></a><span class="lineno"> 673</span>  <a class="code" href="QuEST__internal_8h.html#a3ed30f823a59890be17441d97ce90c5c">statevec_multiControlledMultiRotateZ</a>(qureg, ctrlMask, targMask, angle);</div>
<div class="line"><a name="l00674"></a><span class="lineno"> 674</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00675"></a><span class="lineno"> 675</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00676"></a><span class="lineno"> 676</span>  <a class="code" href="QuEST__internal_8h.html#a3ed30f823a59890be17441d97ce90c5c">statevec_multiControlledMultiRotateZ</a>(qureg, ctrlMask<<shift, targMask<<shift, - angle);</div>
<div class="line"><a name="l00677"></a><span class="lineno"> 677</span>  }</div>
<div class="line"><a name="l00678"></a><span class="lineno"> 678</span>  </div>
<div class="line"><a name="l00679"></a><span class="lineno"> 679</span>  <span class="comment">// @TODO: create actual QASM</span></div>
<div class="line"><a name="l00680"></a><span class="lineno"> 680</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, </div>
<div class="line"><a name="l00681"></a><span class="lineno"> 681</span>  <span class="stringliteral">"Here a %d-control %d-target multiControlledMultiRotateZ of angle %g was performed (QASM not yet implemented)"</span>,</div>
<div class="line"><a name="l00682"></a><span class="lineno"> 682</span>  numControls, numTargets, angle);</div>
<div class="line"><a name="l00683"></a><span class="lineno"> 683</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__cpu_8c_source.html#l03358">statevec_multiControlledMultiRotateZ()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01285">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gad76781842af56821ed4e223bd776f057"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gad76781842af56821ed4e223bd776f057">◆ </a></span>multiControlledPhaseFlip()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void multiControlledPhaseFlip </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControlQubits</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply the multiple-qubit controlled phase flip gate, also known as the multiple-qubit controlled pauliZ gate. </p>
<p>For each state, if all control qubits have value one, multiply the amplitude of that state by -1. This applies the many-qubit unitary: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & \ddots \\ & & & 1 \\ & & & & -1 \end{pmatrix} \]" src="form_75.png"/>
</p>
<p> on the control qubits.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {controls}; \node[draw=none] at (0, 6) {$\vdots$}; \draw (0, 5) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw (0, 4) -- (0, 2); \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 0); \draw (-2,0) -- (2, 0); \draw[fill=black] (0, 0) circle (.2); \end{tikzpicture} \]" src="form_76.png"/>
</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>array of input qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControlQubits</td><td>number of input qubits </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>numControlQubits</code> is outside [1, <code>qureg.numQubitsRepresented</code>)</li>
<li>if any qubit in <code>controlQubits</code> is outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if any qubit in <code>qubits</code> is repeated </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00587">587</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00587"></a><span class="lineno"> 587</span>  {</div>
<div class="line"><a name="l00588"></a><span class="lineno"> 588</span>  <a class="code" href="QuEST__validation_8c.html#a9e7e85cfc36e3ce1f456a840a217bfd9">validateMultiQubits</a>(qureg, controlQubits, numControlQubits, __func__);</div>
<div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  </div>
<div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <a class="code" href="QuEST__internal_8h.html#ac4ee5979d475e8c729294b8ef7e0270d">statevec_multiControlledPhaseFlip</a>(qureg, controlQubits, numControlQubits);</div>
<div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(controlQubits, numControlQubits, shift);</div>
<div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <a class="code" href="QuEST__internal_8h.html#ac4ee5979d475e8c729294b8ef7e0270d">statevec_multiControlledPhaseFlip</a>(qureg, controlQubits, numControlQubits);</div>
<div class="line"><a name="l00595"></a><span class="lineno"> 595</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(controlQubits, numControlQubits, -shift);</div>
<div class="line"><a name="l00596"></a><span class="lineno"> 596</span>  }</div>
<div class="line"><a name="l00597"></a><span class="lineno"> 597</span>  </div>
<div class="line"><a name="l00598"></a><span class="lineno"> 598</span>  <a class="code" href="QuEST__qasm_8c.html#abecd71c919a35e5a87b07ba400edc7c2">qasm_recordMultiControlledGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa228cd6a7ad18928b794ee7ad1f1fc85e">GATE_SIGMA_Z</a>, controlQubits, numControlQubits-1, controlQubits[numControlQubits-1]);</div>
<div class="line"><a name="l00599"></a><span class="lineno"> 599</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00023">GATE_SIGMA_Z</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00317">qasm_recordMultiControlledGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__cpu_8c_source.html#l03718">statevec_multiControlledPhaseFlip()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00444">validateMultiQubits()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01402">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga0832e39058d913ad47af44e97a854446"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga0832e39058d913ad47af44e97a854446">◆ </a></span>multiControlledPhaseShift()</h2>
<div class="memitem">
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<table class="memname">
<tr>
<td class="memname">void multiControlledPhaseShift </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Introduce a phase factor <img class="formulaInl" alt="$ \exp(i \theta) $" src="form_67.png"/> on state <img class="formulaInl" alt="$ |1 \dots 1 \rangle $" src="form_71.png"/> of the passed qubits. </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {controls}; \node[draw=none] at (1, .7) {$\theta$}; \node[draw=none] at (0, 6) {$\vdots$}; \draw (0, 5) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw (0, 4) -- (0, 2); \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 0); \draw (-2,0) -- (2, 0); \draw[fill=black] (0, 0) circle (.2); \end{tikzpicture} \]" src="form_72.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga26baa057f5db8804825c2d611386753b" title="Shift the phase between and of a single qubit by a given angle.">phaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0" title="Introduce a phase factor on state of qubits idQubit1 and idQubit2.">controlledPhaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga2fa310101ecffd6aeba96f77b7d85f56" title="Apply the (two-qubit) controlled phase flip gate, also known as the controlled pauliZ gate.">controlledPhaseFlip()</a></li>
<li><a class="el" href="group__unitary.html#gad76781842af56821ed4e223bd776f057" title="Apply the multiple-qubit controlled phase flip gate, also known as the multiple-qubit controlled paul...">multiControlledPhaseFlip()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>array of qubits to phase shift </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControlQubits</td><td>the length of array <code>controlQubits</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>amount by which to shift the phase in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>numControlQubits</code> is outside [1, <code>qureg.numQubitsRepresented</code>])</li>
<li>if any qubit index in <code>controlQubits</code> is outside [0, <code>qureg.numQubitsRepresented</code>])</li>
<li>if the qubits in <code>controlQubits</code> are not unique </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00510">510</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  {</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <a class="code" href="QuEST__validation_8c.html#a9e7e85cfc36e3ce1f456a840a217bfd9">validateMultiQubits</a>(qureg, controlQubits, numControlQubits, __func__);</div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  </div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  <a class="code" href="QuEST__internal_8h.html#aa662796ea6e0f471143c53becae8c12c">statevec_multiControlledPhaseShift</a>(qureg, controlQubits, numControlQubits, angle);</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(controlQubits, numControlQubits, shift);</div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  <a class="code" href="QuEST__internal_8h.html#aa662796ea6e0f471143c53becae8c12c">statevec_multiControlledPhaseShift</a>(qureg, controlQubits, numControlQubits, -angle);</div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(controlQubits, numControlQubits, -shift);</div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  }</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  </div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  <a class="code" href="QuEST__qasm_8c.html#a1445a08d034806627cc0b5aa0f4f6d3a">qasm_recordMultiControlledParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa4668b36d21aaeba1fb605b73881ca507">GATE_PHASE_SHIFT</a>, controlQubits, numControlQubits-1, controlQubits[numControlQubits-1], angle);</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00032">GATE_PHASE_SHIFT</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00325">qasm_recordMultiControlledParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__cpu_8c_source.html#l03266">statevec_multiControlledPhaseShift()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00444">validateMultiQubits()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01458">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga65c7879947e398690a5428bd43e143e3"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga65c7879947e398690a5428bd43e143e3">◆ </a></span>multiControlledTwoQubitUnitary()</h2>
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<td class="memname">void multiControlledTwoQubitUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix4.html">ComplexMatrix4</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a general multi-controlled two-qubit unitary (including a global phase factor). </p>
<p>Any number of control qubits can be specified, and if all have value 1, the given unitary is applied to the target qubit. This effects the many-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & \ddots \\ & & & u_{00} & u_{01} & u_{02} & u_{03} \\ & & & u_{10} & u_{11} & u_{12} & u_{13} \\ & & & u_{20} & u_{21} & u_{22} & u_{23} \\ & & & u_{30} & u_{31} & u_{32} & u_{33} \end{pmatrix} \]" src="form_215.png"/>
</p>
<p> on the control and target qubits.</p>
<p><code>targetQubit1</code> is treated as the <code>least</code> significant qubit in <code>u</code>, such that a row in <code>u</code> is dotted with the vector <img class="formulaInl" alt="$ |\text{targetQubit2} \;\; \text{targetQubit1}\rangle : \{ |00\rangle, |01\rangle, |10\rangle, |11\rangle \} $" src="form_211.png"/></p>
<p>The passed 4x4 ComplexMatrix must be unitary, otherwise an error is thrown.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target1}; \node[draw=none] at (-3.5, 2) {target2}; \node[draw=none] at (-3.5, 5) {controls}; \node[draw=none] at (0, 8) {$\vdots$}; \draw (0, 7) -- (0, 6); \draw (-2, 6) -- (2, 6); \draw[fill=black] (0, 6) circle (.2); \draw (0, 6) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw(0, 4) -- (0, 3); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-2,2) -- (-1, 2); \draw (1, 2) -- (2, 2); \draw (-1,-1)--(-1,3)--(1,3)--(1,-1)--cycle; \node[draw=none] at (0, 1) {U}; \end{tikzpicture} \]" src="form_216.png"/>
</p>
<p>Note that in distributed mode, this routine requires that each node contains at least 4 amplitudes. This means an q-qubit register (state vector or density matrix) can be distributed by at most 2^q/4 nodes.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix4.html" title="Represents a 4x4 matrix of complex numbers.">ComplexMatrix4</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga3d89916b46bc4aaf23e938022e6c89c1" title="Apply a general controlled two-qubit unitary (including a global phase factor).">controlledTwoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>the control qubits which all must be in state 1 to effect the given unitary </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControlQubits</td><td>the number of control qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit1</td><td>first target qubit, treated as least significant in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit2</td><td>second target qubit, treated as most significant in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit1</code> or <code>targetQubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>targetQubit1</code> equals <code>targetQubit2</code> </li>
<li>if any qubit in <code>controlQubits</code> is outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>controlQubits</code> are not unique</li>
<li>if either <code>targetQubit1</code> and <code>targetQubit2</code> are in <code>controlQubits</code> </li>
<li>if matrix <code>u</code> is not unitary</li>
<li>if each node cannot fit 4 amplitudes in distributed mode </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00282">282</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  {</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <a class="code" href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a>(qureg, controlQubits, numControlQubits, (<span class="keywordtype">int</span>[]) {targetQubit1, targetQubit2}, 2, __func__);</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <a class="code" href="QuEST__validation_8c.html#a654db9d60abdcae26427e7d3b3d9c432">validateTwoQubitUnitaryMatrix</a>(qureg, u, __func__);</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  </div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlQubitsMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(controlQubits, numControlQubits);</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <a class="code" href="QuEST__internal_8h.html#a3eadcb581f2623e21e4967f791d0439c">statevec_multiControlledTwoQubitUnitary</a>(qureg, ctrlQubitsMask, targetQubit1, targetQubit2, u);</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  <a class="code" href="QuEST__internal_8h.html#a3eadcb581f2623e21e4967f791d0439c">statevec_multiControlledTwoQubitUnitary</a>(qureg, ctrlQubitsMask<<shift, targetQubit1+shift, targetQubit2+shift, <a class="code" href="QuEST__common_8c.html#a20d45e85dd49dd3bf6045990b590b24b">getConjugateMatrix4</a>(u));</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  }</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  </div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, <span class="stringliteral">"Here, an undisclosed multi-controlled 2-qubit unitary was applied."</span>);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00110">getConjugateMatrix4()</a>, <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01458">statevec_multiControlledTwoQubitUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00459">validateMultiControlsMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00481">validateTwoQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01513">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gaa700dc9657ade4cf16f1cad1624c5332"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gaa700dc9657ade4cf16f1cad1624c5332">◆ </a></span>multiControlledUnitary()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void multiControlledUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a general multiple-control single-target unitary, which can include a global phase factor. </p>
<p>Any number of control qubits can be specified, and if all have value 1, the given unitary is applied to the target qubit. This effects the many-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & 1 \\\ & & \ddots \\ & & & u_{00} & u_{01}\\ & & & u_{10} & u_{11} \end{pmatrix} \]" src="form_112.png"/>
</p>
<p> on the control and target qubits. The given 2x2 ComplexMatrix must be unitary, otherwise an error is thrown.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 3) {controls}; \node[draw=none] at (-3.5, 0) {target}; \node[draw=none] at (0, 6) {$\vdots$}; \draw (0, 5) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw (0, 4) -- (0, 2); \draw (-2, 2) -- (2, 2); \draw[fill=black] (0, 2) circle (.2); \draw (0, 2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {U}; \end{tikzpicture} \]" src="form_113.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix2.html" title="Represents a 2x2 matrix of complex numbers.">ComplexMatrix2</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa3fb996a5cadd098f4acd8aec955cf9c" title="Apply a general controlled unitary (single control, single target), which can include a global phase ...">controlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga41b946a82982c3fa3dc2a7395665bc90" title="Apply a general single-qubit unitary with multiple control qubits, conditioned upon a specific bit se...">multiStateControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
</ul>
</dd></dl>
<p><br />
</p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>applies unitary if all qubits in this array equal 1 </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControlQubits</td><td>number of control qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>single-qubit unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>numControlQubits</code> is outside [1, <code>qureg.numQubitsRepresented</code>])</li>
<li>if any qubit index (<code>targetQubit</code> or one in <code>controlQubits</code>) is outside [0, <code>qureg.numQubitsRepresented</code>])</li>
<li>if any qubit in <code>controlQubits</code> is repeated</li>
<li>if <code>controlQubits</code> contains <code>targetQubit</code> </li>
<li>if <code>u</code> is not unitary </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00373">373</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  {</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <a class="code" href="QuEST__validation_8c.html#a97f43ad2fe1ffc1f77a9b2af2f5f1cc2">validateMultiControlsTarget</a>(qureg, controlQubits, numControlQubits, targetQubit, __func__);</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <a class="code" href="QuEST__validation_8c.html#a0344fbbb2bb505f7db14b420153f1eb5">validateOneQubitUnitaryMatrix</a>(u, __func__);</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlQubitsMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(controlQubits, numControlQubits);</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlFlipMask = 0;</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  <a class="code" href="QuEST__internal_8h.html#a600bda10463e2078ce746ec28f2d39c9">statevec_multiControlledUnitary</a>(qureg, ctrlQubitsMask, ctrlFlipMask, targetQubit, u);</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  <a class="code" href="QuEST__internal_8h.html#a600bda10463e2078ce746ec28f2d39c9">statevec_multiControlledUnitary</a>(qureg, ctrlQubitsMask<<shift, ctrlFlipMask<<shift, targetQubit+shift, <a class="code" href="QuEST__common_8c.html#ad34d98eeaa6a3cb45e92c696cfd2d1c8">getConjugateMatrix2</a>(u));</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  }</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  </div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <a class="code" href="QuEST__qasm_8c.html#a3a79e4305d35f1756b8438bbd34ea6cc">qasm_recordMultiControlledUnitary</a>(qureg, u, controlQubits, numControlQubits, targetQubit);</div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00105">getConjugateMatrix2()</a>, <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00342">qasm_recordMultiControlledUnitary()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01011">statevec_multiControlledUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00452">validateMultiControlsTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00477">validateOneQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01617">TEST_CASE()</a>.</p>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ga7e58e8131f219f48e5b7410ca8dfe0c0">◆ </a></span>multiQubitNot()</h2>
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<div class="memproto">
<table class="memname">
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<td class="memname">void multiQubitNot </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargs</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a NOT (or Pauli X) gate with multiple target qubits, which has the same effect as (but is much faster than) applying each single-qubit NOT gate in turn. </p>
<p>The ordering within <code>targs</code> has no effect on the operation. </p><blockquote class="doxtable">
<p>This function is equivalent, but significantly faster (approximately <code>numTargs</code> times) than applying <a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a> on each qubit in <code>targs</code> in turn. </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ X_a \otimes X_b \otimes \dots \]" src="form_132.png"/>
</p>
</blockquote>
<p>The effected unitary, if <code>targs</code> happen to be contiguous, has matrix: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} & & & {{\scriptstyle\cdot}^{{\scriptstyle\cdot}^{{\scriptstyle\cdot}}}} \\ & & 1 & \\ & 1 & & \\ {{\scriptstyle\cdot}^{{\scriptstyle\cdot}^{{\scriptstyle\cdot}}}} & & & \end{pmatrix} \]" src="form_133.png"/>
</p>
<p> and circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 1) {targets}; \draw (0, -1) -- (0, 2.4); \draw (-2,2) -- (2, 2); \draw (0, 2) circle (.4); \draw (-2,0) -- (2, 0); \draw (0, 0) circle (.4); \node[draw=none] at (0, -1.5) {$\vdots$}; \end{tikzpicture} \]" src="form_134.png"/>
</p>
<blockquote class="doxtable">
<p>In distributed mode, this operation requires at most a single round of pair-wise communication between nodes, and hence is as efficient as <a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a>. </p>
</blockquote>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gafd81a9217fb7d21c365443442492b2dc" title="Apply a NOT (or Pauli X) gate with multiple control and target qubits.">multiControlledMultiQubitNot()</a></li>
<li><a class="el" href="group__unitary.html#gaa5a138473a4433c853c6e66e7aabc237" title="Apply the controlled not (single control, single target) gate, also known as the c-X,...">controlledNot()</a></li>
<li><a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>a state-vector or density matrix to modify </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targs</td><td>a list of the qubits to be targeted by the X gates </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargs</td><td>the length of list <code>targs</code> </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if any qubit in <code>targs</code> is invalid, i.e. outside <b>[0, </b><code>qureg.numQubitsRepresented</code><b>)</b></li>
<li>if <code>targs</code> contain any repetitions</li>
<li>if <code>numTargs</code> <b>< 1</b></li>
<li>if <code>numTargs</code> <b>></b><code>qureg.numQubitsRepresented</code> </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>targs</code> contains fewer elements than <code>numTargs</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00536">536</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  {</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  <a class="code" href="QuEST__validation_8c.html#a6776217a5f7ba38b56175cf6db0f96e0">validateMultiTargets</a>(qureg, targs, numTargs, __func__);</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  </div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> targMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(targs, numTargs);</div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <a class="code" href="QuEST__internal_8h.html#a13ecc24b355a5213d745651cde56bd71">statevec_multiControlledMultiQubitNot</a>(qureg, 0, targMask);</div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  <a class="code" href="QuEST__internal_8h.html#a13ecc24b355a5213d745651cde56bd71">statevec_multiControlledMultiQubitNot</a>(qureg, 0, targMask<<shift);</div>
<div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  }</div>
<div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  </div>
<div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <a class="code" href="QuEST__qasm_8c.html#a2275a3f14e8853261533ee41416ae19d">qasm_recordMultiControlledMultiQubitNot</a>(qureg, NULL, 0, targs, numTargs);</div>
<div class="line"><a name="l00547"></a><span class="lineno"> 547</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00382">qasm_recordMultiControlledMultiQubitNot()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01097">statevec_multiControlledMultiQubitNot()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00428">validateMultiTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01688">TEST_CASE()</a>.</p>
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</div>
<a id="ga20bf9b8a71b8a3ee4651e9497e6d1f4f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga20bf9b8a71b8a3ee4651e9497e6d1f4f">◆ </a></span>multiQubitUnitary()</h2>
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<table class="memname">
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<td class="memname">void multiQubitUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargs</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrixN.html">ComplexMatrixN</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubits. </p>
<p>The first target qubit in <code>targs</code> is treated as <b>least</b> significant in <code>u</code>. For example, </p><div class="fragment"><div class="line"><a class="code" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f">multiQubitUnitary</a>(qureg, (<span class="keywordtype">int</span> []) {a, b, c}, 3, u);</div>
</div><!-- fragment --><p>will invoke multiplication </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} u_{00} & u_{01} & u_{02} & u_{03} & u_{04} & u_{05} & u_{06} & u_{07} \\ u_{10} & u_{11} & u_{12} & u_{13} & u_{14} & u_{15} & u_{16} & u_{17} \\ u_{20} & u_{21} & u_{22} & u_{23} & u_{24} & u_{25} & u_{26} & u_{27} \\ u_{30} & u_{31} & u_{32} & u_{33} & u_{34} & u_{35} & u_{36} & u_{37} \\ u_{40} & u_{41} & u_{42} & u_{43} & u_{44} & u_{45} & u_{46} & u_{47} \\ u_{50} & u_{51} & u_{52} & u_{53} & u_{54} & u_{55} & u_{56} & u_{57} \\ u_{60} & u_{61} & u_{62} & u_{63} & u_{64} & u_{65} & u_{66} & u_{67} \\ u_{70} & u_{71} & u_{72} & u_{73} & u_{74} & u_{75} & u_{76} & u_{77} \\ \end{pmatrix} \begin{pmatrix} |cba\rangle = |000\rangle \\ |cba\rangle = |001\rangle \\ |cba\rangle = |010\rangle \\ |cba\rangle = |011\rangle \\ |cba\rangle = |100\rangle \\ |cba\rangle = |101\rangle \\ |cba\rangle = |110\rangle \\ |cba\rangle = |111\rangle \end{pmatrix} \]" src="form_217.png"/>
</p>
<p>The passed ComplexMatrix must be unitary and be a compatible size with the specified number of target qubits, otherwise an error is thrown. </p><blockquote class="doxtable">
<p>To left-multiply a non-unitary <a class="el" href="structComplexMatrixN.html" title="Represents a general 2^N by 2^N matrix of complex numbers.">ComplexMatrixN</a>, use <a class="el" href="group__operator.html#ga358e7094a98851afa86d27f0147e32a1" title="Apply a general N-by-N matrix, which may be non-unitary, on any number of target qubits.">applyMatrixN()</a>. </p>
</blockquote>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 1) {targets}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-2,2) -- (-1, 2); \draw (1, 2) -- (2, 2); \draw (-1,-1)--(-1,3)--(1,3)--(1,-1); \node[draw=none] at (0, 1) {U}; \node[draw=none] at (0, -1) {$\vdots$}; \end{tikzpicture} \]" src="form_218.png"/>
</p>
<p>Note that in multithreaded mode, each thread will clone 2^<code>numTargs</code> amplitudes, and store these in the runtime stack. Using t threads, the total memory overhead of this function is t*2^<code>numTargs</code>. For many targets (e.g. 16 qubits), this may cause a stack-overflow / seg-fault (e.g. on a 1 MiB stack).</p>
<p>Note too that in distributed mode, this routine requires that each node contains at least 2^<code>numTargs</code> amplitudes in the register. This means an q-qubit register (state vector or density matrix) can be distributed by at most 2^q / 2^<code>numTargs</code> nodes.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__type.html#ga815103261fb22ea9690e1427571df00e" title="Allocate dynamic memory for a square complex matrix of any size, which can be passed to functions lik...">createComplexMatrixN()</a></li>
<li><a class="el" href="group__unitary.html#gaeb975903209000ebbaf50ef1cc353a79" title="Apply a general controlled multi-qubit unitary (including a global phase factor).">controlledMultiQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga3ad6c477edcdbc845fc1143e860fda08" title="Apply a general multi-controlled multi-qubit unitary (including a global phase factor).">multiControlledMultiQubitUnitary()</a></li>
<li><a class="el" href="group__operator.html#ga358e7094a98851afa86d27f0147e32a1" title="Apply a general N-by-N matrix, which may be non-unitary, on any number of target qubits.">applyMatrixN()</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targs</td><td>a list of the target qubits, ordered least significant to most in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargs</td><td>the number of target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if any index in <code>targs</code> is outside of [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>targs</code> are not unique</li>
<li>if matrix <code>u</code> is not unitary</li>
<li>if <code>u</code> is not of a compatible size with <code>numTargs</code> </li>
<li>if a node cannot fit the required number of target amplitudes in distributed mode </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00296">296</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  {</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <a class="code" href="QuEST__validation_8c.html#a6776217a5f7ba38b56175cf6db0f96e0">validateMultiTargets</a>(qureg, targs, numTargs, __func__);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <a class="code" href="QuEST__validation_8c.html#ab9947ff071a0c019f715f04b3833dcfd">validateMultiQubitUnitaryMatrix</a>(qureg, u, numTargs, __func__);</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  </div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  <a class="code" href="QuEST__common_8c.html#a7a76950824f17e821415070a4bfdad5b">statevec_multiQubitUnitary</a>(qureg, targs, numTargs, u);</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targs, numTargs, shift);</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <a class="code" href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a>(u);</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <a class="code" href="QuEST__common_8c.html#a7a76950824f17e821415070a4bfdad5b">statevec_multiQubitUnitary</a>(qureg, targs, numTargs, u);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targs, numTargs, -shift);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <a class="code" href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a>(u);</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  }</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  </div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, <span class="stringliteral">"Here, an undisclosed multi-qubit unitary was applied."</span>);</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00115">setConjugateMatrixN()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__common_8c_source.html#l00573">statevec_multiQubitUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00502">validateMultiQubitUnitaryMatrix()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00428">validateMultiTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01755">TEST_CASE()</a>.</p>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ga34aa4865c92f9aa5d898c91286c9eca5">◆ </a></span>multiRotatePauli()</h2>
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<td class="memname">void multiRotatePauli </td>
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<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>targetQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">enum <a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028">pauliOpType</a> * </td>
<td class="paramname"><em>targetPaulis</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numTargets</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
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<td>)</td>
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<p>Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubits. </p>
<p>This is the unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \exp \left( - i \, \frac{\theta}{2} \; \bigotimes_{j}^{\text{numTargets}} \hat{\sigma}_j\right) \]" src="form_184.png"/>
</p>
<p> where <img class="formulaInl" alt="$\theta = $" src="form_185.png"/><code>angle</code> and <img class="formulaInl" alt="$\hat{\sigma}_j \in \{X, Y, Z\}$" src="form_186.png"/> is a Pauli operator <a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028" title="Codes for specifying Pauli operators.">pauliOpType</a> operating upon the corresponding qubit <code>targetQubits</code>.</p>
<p>For example: </p><div class="fragment"><div class="line"><a class="code" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5">multiRotatePauli</a>(qureg, (<span class="keywordtype">int</span>[]) {4,5,8,9}, (<span class="keywordtype">int</span>[]) {0,1,2,3}, 4, .1)</div>
</div><!-- fragment --><p>effects </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \exp \left( - i \, (0.1/2) \; X_5 \, Y_8 \, Z_9 \right) \]" src="form_187.png"/>
</p>
<p> on <code>qureg</code>, where unspecified qubits (along with those targeted by <code>PAULI_I</code>) are assumed to receive the identity operator (excluded from exponentiation). </p><blockquote class="doxtable">
<p>This means specifying <code>PAULI_I</code> does <em>not</em> induce a global phase factor <img class="formulaInl" alt="$\exp(-i \theta/2)$" src="form_188.png"/>. Hence, if all <code>targetPaulis</code> are identity, then this function does nothing to <code>qureg</code>. Specifying <code>PAULI_I</code> on a qubit is superfluous but allowed for convenience. </p>
</blockquote>
<p>This function effects the Pauli gadget by first rotating the qubits which are nominated to receive <code>X</code> or <code>Y</code> Paulis into alternate basis, performing <a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a> on all target qubits, then restoring the original basis.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gab2ececaa253252e1b1cdb18a8452704a" title="Apply a multi-controlled multi-target multi-Pauli rotation, also known as a controlled Pauli gadget.">multiControlledMultiRotatePauli()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145" title="Rotate a single qubit by a given angle around a given Vector on the Bloch-sphere.">rotateAroundAxis()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubits</td><td>a list of the indices of the target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetPaulis</td><td>a list of the Pauli operators (<a class="el" href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028" title="Codes for specifying Pauli operators.">pauliOpType</a>) to apply to the corresponding qubits in <code>targetQubits</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numTargets</td><td>number of target qubits, i.e. the length of <code>targetQubits</code> and <code>targetPaulis</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>the angle by which the multi-qubit state is rotated </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>numTargets</code> is outside [1, <code>qureg.numQubitsRepresented</code>)</li>
<li>if any qubit in <code>targetQubits</code> is outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if any qubit in <code>targetQubits</code> is repeated</li>
<li>if any element of <code>targetPaulis</code> is not one of <code>PAULI_I</code>, <code>PAULI_X</code>, <code>PAULI_Y</code>, <code>PAULI_Z</code> </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>targetQubits</code> contains fewer elements than <code>numTargets</code> </li>
<li>if <code>targetPaulis</code> contains fewer elements than <code>numTargets</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00685">685</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00685"></a><span class="lineno"> 685</span>  {</div>
<div class="line"><a name="l00686"></a><span class="lineno"> 686</span>  <a class="code" href="QuEST__validation_8c.html#a6776217a5f7ba38b56175cf6db0f96e0">validateMultiTargets</a>(qureg, targetQubits, numTargets, __func__);</div>
<div class="line"><a name="l00687"></a><span class="lineno"> 687</span>  <a class="code" href="QuEST__validation_8c.html#aa194ba5f5c6e19c6caa4c715b3dbefcc">validatePauliCodes</a>(targetPaulis, numTargets, __func__);</div>
<div class="line"><a name="l00688"></a><span class="lineno"> 688</span>  </div>
<div class="line"><a name="l00689"></a><span class="lineno"> 689</span>  <span class="keywordtype">int</span> conj=0;</div>
<div class="line"><a name="l00690"></a><span class="lineno"> 690</span>  <a class="code" href="QuEST__common_8c.html#a2153d8611247dd3a2ef483355265cc99">statevec_multiRotatePauli</a>(qureg, targetQubits, targetPaulis, numTargets, angle, conj);</div>
<div class="line"><a name="l00691"></a><span class="lineno"> 691</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00692"></a><span class="lineno"> 692</span>  conj = 1;</div>
<div class="line"><a name="l00693"></a><span class="lineno"> 693</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00694"></a><span class="lineno"> 694</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targetQubits, numTargets, shift);</div>
<div class="line"><a name="l00695"></a><span class="lineno"> 695</span>  <a class="code" href="QuEST__common_8c.html#a2153d8611247dd3a2ef483355265cc99">statevec_multiRotatePauli</a>(qureg, targetQubits, targetPaulis, numTargets, angle, conj);</div>
<div class="line"><a name="l00696"></a><span class="lineno"> 696</span>  <a class="code" href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a>(targetQubits, numTargets, -shift);</div>
<div class="line"><a name="l00697"></a><span class="lineno"> 697</span>  }</div>
<div class="line"><a name="l00698"></a><span class="lineno"> 698</span>  </div>
<div class="line"><a name="l00699"></a><span class="lineno"> 699</span>  <span class="comment">// @TODO: create actual QASM</span></div>
<div class="line"><a name="l00700"></a><span class="lineno"> 700</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, </div>
<div class="line"><a name="l00701"></a><span class="lineno"> 701</span>  <span class="stringliteral">"Here a %d-qubit multiRotatePauli of angle %g was performed (QASM not yet implemented)"</span>,</div>
<div class="line"><a name="l00702"></a><span class="lineno"> 702</span>  numTargets, angle);</div>
<div class="line"><a name="l00703"></a><span class="lineno"> 703</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00156">shiftIndices()</a>, <a class="el" href="QuEST__common_8c_source.html#l00414">statevec_multiRotatePauli()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00428">validateMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00599">validatePauliCodes()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__operators_8cpp_source.html#l03500">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga3250d0d95b5d755cad542a6a2372b894">◆ </a></span>multiRotateZ()</h2>
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<td class="memname">void multiRotateZ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>qubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits. </p>
<p>This is the unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \exp \left( - i \, \frac{\theta}{2} \; \bigotimes_{j}^{\text{numQubits}} Z_j\right) \]" src="form_181.png"/>
</p>
<p> where the Pauli Z gates operate the qubits listed in <code>qubits</code>, and cause rotations of <img class="formulaInl" alt="$\theta =$" src="form_182.png"/> <code>angle</code>.</p>
<blockquote class="doxtable">
<p>All qubits not appearing in <code>qubits</code> are assumed to receive the identity operator. </p>
</blockquote>
<p>This has the effect of premultiplying every amplitude with <img class="formulaInl" alt="$\exp(\pm i \theta/2)$" src="form_183.png"/> where the sign is determined by the parity of the target qubits for that amplitude.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga1e5dd165b402e97abaa0b807026527f2" title="Apply a multi-controlled multi-target Z rotation, also known as a controlled phase gadget.">multiControlledMultiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
<li><a class="el" href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120" title="Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere.">controlledRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">qubits</td><td>a list of the indices of the target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numQubits</td><td>number of target qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>the angle by which the multi-qubit state is rotated around the Z axis </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>numQubits</code> is outside [1, <code>qureg.numQubitsRepresented</code>])</li>
<li>if any qubit in <code>qubits</code> is outside [0, <code>qureg.numQubitsRepresented</code>])</li>
<li>if any qubit in <code>qubits</code> is repeated </li>
</ul>
</td></tr>
<tr><td class="paramname">segmentation-fault</td><td><ul>
<li>if <code>qubits</code> contains fewer elements than <code>numQubits</code> </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00652">652</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00652"></a><span class="lineno"> 652</span>  {</div>
<div class="line"><a name="l00653"></a><span class="lineno"> 653</span>  <a class="code" href="QuEST__validation_8c.html#a6776217a5f7ba38b56175cf6db0f96e0">validateMultiTargets</a>(qureg, qubits, numQubits, __func__);</div>
<div class="line"><a name="l00654"></a><span class="lineno"> 654</span>  </div>
<div class="line"><a name="l00655"></a><span class="lineno"> 655</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> mask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(qubits, numQubits);</div>
<div class="line"><a name="l00656"></a><span class="lineno"> 656</span>  <a class="code" href="QuEST__internal_8h.html#a8d88b4ed94ab024e5e7b2f1f4f505b44">statevec_multiRotateZ</a>(qureg, mask, angle);</div>
<div class="line"><a name="l00657"></a><span class="lineno"> 657</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00658"></a><span class="lineno"> 658</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00659"></a><span class="lineno"> 659</span>  <a class="code" href="QuEST__internal_8h.html#a8d88b4ed94ab024e5e7b2f1f4f505b44">statevec_multiRotateZ</a>(qureg, mask << shift, -angle);</div>
<div class="line"><a name="l00660"></a><span class="lineno"> 660</span>  }</div>
<div class="line"><a name="l00661"></a><span class="lineno"> 661</span>  </div>
<div class="line"><a name="l00662"></a><span class="lineno"> 662</span>  <span class="comment">// @TODO: create actual QASM</span></div>
<div class="line"><a name="l00663"></a><span class="lineno"> 663</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, </div>
<div class="line"><a name="l00664"></a><span class="lineno"> 664</span>  <span class="stringliteral">"Here a %d-qubit multiRotateZ of angle %g was performed (QASM not yet implemented)"</span>,</div>
<div class="line"><a name="l00665"></a><span class="lineno"> 665</span>  numQubits, angle);</div>
<div class="line"><a name="l00666"></a><span class="lineno"> 666</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__cpu_8c_source.html#l03316">statevec_multiRotateZ()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00428">validateMultiTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l01977">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga41b946a82982c3fa3dc2a7395665bc90"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga41b946a82982c3fa3dc2a7395665bc90">◆ </a></span>multiStateControlledUnitary()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void multiStateControlledUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>controlState</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>numControlQubits</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply a general single-qubit unitary with multiple control qubits, conditioned upon a specific bit sequence. </p>
<p>Any number of control qubits can be specified, along with their classical state (<code>0</code> or <code>1</code>) to condition upon. Only amplitudes of computational basis states for which <code>controlQubits</code> have corresponding bit values <code>controlState</code> are modified by <code>u</code>.</p>
<blockquote class="doxtable">
<p>This function is equivalent (albeit faster) to applying <a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a> on each of the control qubits which are conditioned on outcome <code>0</code>, calling <a class="el" href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332" title="Apply a general multiple-control single-target unitary, which can include a global phase factor.">multiControlledUnitary()</a>, then re-appplying <a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a> on the same qubits. </p>
</blockquote>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 3) {controls}; \node[draw=none] at (-3.5, 0) {target}; \node[draw=none] at (0, 6) {$\vdots$}; \draw (0, 5) -- (0, 4); \draw (-2, 4) -- (2, 4); \draw[fill=black] (0, 4) circle (.2); \draw (0, 4) -- (0, 2); \draw (-2, 2) -- (2, 2); \draw[fill=white] (0, 2) circle (.2); \draw (0, 2-.2) -- (0, 1); \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {U}; \end{tikzpicture} \]" src="form_180.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix2.html" title="Represents a 2x2 matrix of complex numbers.">ComplexMatrix2</a></li>
<li><a class="el" href="group__unitary.html#ga78b814256f851cac70fdf3cbf9cfc206" title="Apply a general single-qubit unitary (including a global phase factor).">unitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa3fb996a5cadd098f4acd8aec955cf9c" title="Apply a general controlled unitary (single control, single target), which can include a global phase ...">controlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332" title="Apply a general multiple-control single-target unitary, which can include a global phase factor.">multiControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlQubits</td><td>the indices of the control qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">controlState</td><td>the bit values (0 or 1) of each control qubit, upon which to condition </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">numControlQubits</td><td>number of control qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate the unitary upon </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>single-qubit unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>numControlQubits</code> is outside [1, <code>qureg.numQubitsRepresented</code>])</li>
<li>if any qubit index (<code>targetQubit</code> or one in <code>controlQubits</code>) is outside [0, <code>qureg.numQubitsRepresented</code>]),</li>
<li>if any qubit in <code>controlQubits</code> is repeated</li>
<li>if <code>controlQubits</code> contains <code>targetQubit</code> </li>
<li>if any element of <code>controlState</code> is not a bit (<code>0</code> or <code>1</code>)</li>
<li>if <code>u</code> is not unitary </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00388">388</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  {</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  <a class="code" href="QuEST__validation_8c.html#a97f43ad2fe1ffc1f77a9b2af2f5f1cc2">validateMultiControlsTarget</a>(qureg, controlQubits, numControlQubits, targetQubit, __func__);</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  <a class="code" href="QuEST__validation_8c.html#a0344fbbb2bb505f7db14b420153f1eb5">validateOneQubitUnitaryMatrix</a>(u, __func__);</div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <a class="code" href="QuEST__validation_8c.html#a0bd6443ea0f5e36738f3b39b72080b6e">validateControlState</a>(controlState, numControlQubits, __func__);</div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  </div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlQubitsMask = <a class="code" href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a>(controlQubits, numControlQubits);</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  <span class="keywordtype">long</span> <span class="keywordtype">long</span> <span class="keywordtype">int</span> ctrlFlipMask = <a class="code" href="QuEST__common_8c.html#a6fa6f1bc617e9fef3cd87ecc3677a02b">getControlFlipMask</a>(controlQubits, controlState, numControlQubits);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <a class="code" href="QuEST__internal_8h.html#a600bda10463e2078ce746ec28f2d39c9">statevec_multiControlledUnitary</a>(qureg, ctrlQubitsMask, ctrlFlipMask, targetQubit, u);</div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  <a class="code" href="QuEST__internal_8h.html#a600bda10463e2078ce746ec28f2d39c9">statevec_multiControlledUnitary</a>(qureg, ctrlQubitsMask<<shift, ctrlFlipMask<<shift, targetQubit+shift, <a class="code" href="QuEST__common_8c.html#ad34d98eeaa6a3cb45e92c696cfd2d1c8">getConjugateMatrix2</a>(u));</div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  }</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  </div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <a class="code" href="QuEST__qasm_8c.html#a9975b6f54f4090cdf851958bc2b37230">qasm_recordMultiStateControlledUnitary</a>(qureg, u, controlQubits, controlState, numControlQubits, targetQubit);</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00105">getConjugateMatrix2()</a>, <a class="el" href="QuEST__common_8c_source.html#l00060">getControlFlipMask()</a>, <a class="el" href="QuEST__common_8c_source.html#l00050">getQubitBitMask()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00363">qasm_recordMultiStateControlledUnitary()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01011">statevec_multiControlledUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00468">validateControlState()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00452">validateMultiControlsTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00477">validateOneQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02050">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga4193c14cfb918fa3291fb0648058d63e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga4193c14cfb918fa3291fb0648058d63e">◆ </a></span>pauliX()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void pauliX </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate. </p>
<p>This is a rotation of <img class="formulaInl" alt="$\pi$" src="form_114.png"/> around the x-axis on the Bloch sphere. I.e. </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \]" src="form_115.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (2, 0); \draw (0, 0) circle (.5); \draw (0, .5) -- (0, -.5); \end{tikzpicture} \]" src="form_116.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga8e0f03e745778a89d6f59c3c25e32df8" title="Apply the single-qubit Pauli-Y (also known as the Y or sigma-Y) gate.">pauliY()</a></li>
<li><a class="el" href="group__unitary.html#ga5d80b490e3910aa737a81bb597cdfcc9" title="Apply the single-qubit Pauli-Z (also known as the Z, sigma-Z or phase-flip) gate.">pauliZ()</a></li>
<li><a class="el" href="group__unitary.html#gaa5a138473a4433c853c6e66e7aabc237" title="Apply the controlled not (single control, single target) gate, also known as the c-X,...">controlledNot()</a></li>
<li><a class="el" href="group__unitary.html#ga7e58e8131f219f48e5b7410ca8dfe0c0" title="Apply a NOT (or Pauli X) gate with multiple target qubits, which has the same effect as (but is much ...">multiQubitNot()</a></li>
<li><a class="el" href="group__unitary.html#gafd81a9217fb7d21c365443442492b2dc" title="Apply a NOT (or Pauli X) gate with multiple control and target qubits.">multiControlledMultiQubitNot()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00432">432</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00432"></a><span class="lineno"> 432</span>  {</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  </div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>  <a class="code" href="QuEST__internal_8h.html#a1c82b5e914a8a39c5c7b782dbc16fa76">statevec_pauliX</a>(qureg, targetQubit);</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <a class="code" href="QuEST__internal_8h.html#a1c82b5e914a8a39c5c7b782dbc16fa76">statevec_pauliX</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>);</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  }</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  </div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <a class="code" href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa13c9487aed515148e7594e35eb8dcc55">GATE_SIGMA_X</a>, targetQubit);</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00021">GATE_SIGMA_X</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00179">qasm_recordGate()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01048">statevec_pauliX()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02159">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga8e0f03e745778a89d6f59c3c25e32df8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga8e0f03e745778a89d6f59c3c25e32df8">◆ </a></span>pauliY()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void pauliY </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply the single-qubit Pauli-Y (also known as the Y or sigma-Y) gate. </p>
<p>This is a rotation of <img class="formulaInl" alt="$\pi$" src="form_114.png"/> around the Y-axis on the Bloch sphere. I.e. </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \]" src="form_117.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$\sigma_y$}; \end{tikzpicture} \]" src="form_118.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a></li>
<li><a class="el" href="group__unitary.html#ga5d80b490e3910aa737a81bb597cdfcc9" title="Apply the single-qubit Pauli-Z (also known as the Z, sigma-Z or phase-flip) gate.">pauliZ()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00443">443</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  {</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  </div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <a class="code" href="QuEST__internal_8h.html#af1cca787f3b0e0c91ffb2495f9ad8d5a">statevec_pauliY</a>(qureg, targetQubit);</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <a class="code" href="QuEST__internal_8h.html#a81fbd2eccd0d0e5a3cece4df2f96cb92">statevec_pauliYConj</a>(qureg, targetQubit + qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>);</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  }</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <a class="code" href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725faa29b98cbb581abf5ec338a1763de7a1b">GATE_SIGMA_Y</a>, targetQubit);</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00022">GATE_SIGMA_Y</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00179">qasm_recordGate()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01142">statevec_pauliY()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01167">statevec_pauliYConj()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02198">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga5d80b490e3910aa737a81bb597cdfcc9"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga5d80b490e3910aa737a81bb597cdfcc9">◆ </a></span>pauliZ()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void pauliZ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Apply the single-qubit Pauli-Z (also known as the Z, sigma-Z or phase-flip) gate. </p>
<p>This is a rotation of <img class="formulaInl" alt="$\pi$" src="form_114.png"/> around the Z-axis (a phase shift) on the Bloch sphere. I.e. </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \]" src="form_119.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$\sigma_z$}; \end{tikzpicture} \]" src="form_120.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga26baa057f5db8804825c2d611386753b" title="Shift the phase between and of a single qubit by a given angle.">phaseShift()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga4193c14cfb918fa3291fb0648058d63e" title="Apply the single-qubit Pauli-X (also known as the X, sigma-X, NOT or bit-flip) gate.">pauliX()</a></li>
<li><a class="el" href="group__unitary.html#ga8e0f03e745778a89d6f59c3c25e32df8" title="Apply the single-qubit Pauli-Y (also known as the Y or sigma-Y) gate.">pauliY()</a></li>
<li><a class="el" href="group__unitary.html#ga2fa310101ecffd6aeba96f77b7d85f56" title="Apply the (two-qubit) controlled phase flip gate, also known as the controlled pauliZ gate.">controlledPhaseFlip()</a></li>
<li><a class="el" href="group__unitary.html#gad76781842af56821ed4e223bd776f057" title="Apply the multiple-qubit controlled phase flip gate, also known as the multiple-qubit controlled paul...">multiControlledPhaseFlip()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00454">454</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  {</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  </div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <a class="code" href="QuEST__common_8c.html#ab14df201e5c05527dc77cfeb6f583042">statevec_pauliZ</a>(qureg, targetQubit);</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <a class="code" href="QuEST__common_8c.html#ab14df201e5c05527dc77cfeb6f583042">statevec_pauliZ</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>);</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  }</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <a class="code" href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa228cd6a7ad18928b794ee7ad1f1fc85e">GATE_SIGMA_Z</a>, targetQubit);</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00023">GATE_SIGMA_Z</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00179">qasm_recordGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00261">statevec_pauliZ()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02237">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga26baa057f5db8804825c2d611386753b"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga26baa057f5db8804825c2d611386753b">◆ </a></span>phaseShift()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void phaseShift </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Shift the phase between <img class="formulaInl" alt="$ |0\rangle $" src="form_62.png"/> and <img class="formulaInl" alt="$ |1\rangle $" src="form_63.png"/> of a single qubit by a given angle. </p>
<blockquote class="doxtable">
<p>This is equivalent to a Z-axis rotation of the Bloch-sphere up to a global phase factor. </p>
</blockquote>
<p>For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/>, this effects single-qubit unitary </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 & 0 \\ 0 & \exp(i \theta) \end{pmatrix} \]" src="form_65.png"/>
</p>
<p> with circuit diagram </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-4, 0) {targetQubit}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_\theta$}; \end{tikzpicture} \]" src="form_66.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga7214a79aa22ae7a50ad6f38615968cb0" title="Introduce a phase factor on state of qubits idQubit1 and idQubit2.">controlledPhaseShift()</a></li>
<li><a class="el" href="group__unitary.html#ga0832e39058d913ad47af44e97a854446" title="Introduce a phase factor on state of the passed qubits.">multiControlledPhaseShift()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to undergo a phase shift </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>amount by which to shift the phase in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li><code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>). </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00487">487</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  {</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  </div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  <a class="code" href="QuEST__common_8c.html#a5ef139196852f92fe8271c82964eadff">statevec_phaseShift</a>(qureg, targetQubit, angle);</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <a class="code" href="QuEST__common_8c.html#a5ef139196852f92fe8271c82964eadff">statevec_phaseShift</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>, -angle);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  }</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  </div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <a class="code" href="QuEST__qasm_8c.html#aabeb3e9ec6b2f30938c4cf9592e624fa">qasm_recordParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa4668b36d21aaeba1fb605b73881ca507">GATE_PHASE_SHIFT</a>, targetQubit, angle);</div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00032">GATE_PHASE_SHIFT</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00187">qasm_recordParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00254">statevec_phaseShift()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02276">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga4c708f066b244801e10f538b48b90145"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga4c708f066b244801e10f538b48b90145">◆ </a></span>rotateAroundAxis()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void rotateAroundAxis </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>rotQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structVector.html">Vector</a> </td>
<td class="paramname"><em>axis</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Rotate a single qubit by a given angle around a given <a class="el" href="structVector.html">Vector</a> on the Bloch-sphere. </p>
<p><br />
The vector must not be zero (else an error is thrown), but needn't be unit magnitude, since it will be normalised by QuEST.</p>
<p>For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/> and axis vector <img class="formulaInl" alt="$\vec{n}$" src="form_101.png"/>, applies <img class="formulaInl" alt="$R_{\hat{n}} = \exp \left(- i \frac{\theta}{2} \hat{n} \cdot \vec{\sigma} \right) $" src="form_102.png"/> where <img class="formulaInl" alt="$\vec{\sigma}$" src="form_103.png"/> is the vector of Pauli matrices.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga0c84c429cb1d7e2596706c1804dd9cba" title="Applies a controlled rotation by a given angle around a given vector on the Bloch-sphere.">controlledRotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rotQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate in radians </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">axis</td><td>vector around which to rotate (can be non-unit; will be normalised) </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>rotQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>axis</code> is the zero vector </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00601">601</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00601"></a><span class="lineno"> 601</span>  {</div>
<div class="line"><a name="l00602"></a><span class="lineno"> 602</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, rotQubit, __func__);</div>
<div class="line"><a name="l00603"></a><span class="lineno"> 603</span>  <a class="code" href="QuEST__validation_8c.html#a782c6f57939eeb72b7be8e247979f3be">validateVector</a>(axis, __func__);</div>
<div class="line"><a name="l00604"></a><span class="lineno"> 604</span>  </div>
<div class="line"><a name="l00605"></a><span class="lineno"> 605</span>  <a class="code" href="QuEST__common_8c.html#adf5fbea75826cde7d86fd7c31bcf3dec">statevec_rotateAroundAxis</a>(qureg, rotQubit, angle, axis);</div>
<div class="line"><a name="l00606"></a><span class="lineno"> 606</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00607"></a><span class="lineno"> 607</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00608"></a><span class="lineno"> 608</span>  <a class="code" href="QuEST__common_8c.html#a2cbfe9f416d4d8acb56213841f62cb53">statevec_rotateAroundAxisConj</a>(qureg, rotQubit+shift, angle, axis);</div>
<div class="line"><a name="l00609"></a><span class="lineno"> 609</span>  }</div>
<div class="line"><a name="l00610"></a><span class="lineno"> 610</span>  </div>
<div class="line"><a name="l00611"></a><span class="lineno"> 611</span>  <a class="code" href="QuEST__qasm_8c.html#a42607270d63948acf84d6def787213e8">qasm_recordAxisRotation</a>(qureg, angle, axis, rotQubit);</div>
<div class="line"><a name="l00612"></a><span class="lineno"> 612</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00224">qasm_recordAxisRotation()</a>, <a class="el" href="QuEST__common_8c_source.html#l00314">statevec_rotateAroundAxis()</a>, <a class="el" href="QuEST__common_8c_source.html#l00321">statevec_rotateAroundAxisConj()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00511">validateVector()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02316">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga8886a3793b21622c48cf3bad6e15082d"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga8886a3793b21622c48cf3bad6e15082d">◆ </a></span>rotateX()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void rotateX </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>rotQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere. </p>
<p>For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/>, applies </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} \cos\theta/2 & -i \sin \theta/2\\ -i \sin \theta/2 & \cos \theta/2 \end{pmatrix} \]" src="form_95.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {rot}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_x(\theta)$}; \end{tikzpicture} \]" src="form_96.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga13f904b417f647c70d163770e65906fc" title="Applies a controlled rotation by a given angle around the X-axis of the Bloch-sphere.">controlledRotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145" title="Rotate a single qubit by a given angle around a given Vector on the Bloch-sphere.">rotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rotQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>rotQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00187">187</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  {</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <a class="code" href="QuEST__common_8c.html#ab8687e6ea5cf35503c223051837f3b94">statevec_rotateX</a>(qureg, targetQubit, angle);</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <a class="code" href="QuEST__common_8c.html#ab8687e6ea5cf35503c223051837f3b94">statevec_rotateX</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>, -angle);</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  }</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  </div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <a class="code" href="QuEST__qasm_8c.html#aabeb3e9ec6b2f30938c4cf9592e624fa">qasm_recordParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fada07505b73935b2788032efd30a1a361">GATE_ROTATE_X</a>, targetQubit, angle);</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00027">GATE_ROTATE_X</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00187">qasm_recordParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00296">statevec_rotateX()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02372">TEST_CASE()</a>.</p>
</div>
</div>
<a id="ga34312ff52cc28bcab3cbd2ff338fd081"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ga34312ff52cc28bcab3cbd2ff338fd081">◆ </a></span>rotateY()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void rotateY </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>rotQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere. </p>
<p>For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/>, applies </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} \cos\theta/2 & - \sin \theta/2\\ \sin \theta/2 & \cos \theta/2 \end{pmatrix} \]" src="form_97.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {rot}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_y(\theta)$}; \end{tikzpicture} \]" src="form_98.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gafbbded98b7233f5da06d74d1db5cbfdb" title="Applies a controlled rotation by a given angle around the Y-axis of the Bloch-sphere.">controlledRotateY()</a></li>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#gab23a8b022ec83b9d423961ca87cd8cb5" title="Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase s...">rotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145" title="Rotate a single qubit by a given angle around a given Vector on the Bloch-sphere.">rotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rotQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname">invalidQuESTInputError</td><td>if <code>rotQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>). </td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc, debug) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00198">198</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  {</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  </div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <a class="code" href="QuEST__common_8c.html#a1f0db2800d13b6c2b120e05129cd13cb">statevec_rotateY</a>(qureg, targetQubit, angle);</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <a class="code" href="QuEST__common_8c.html#a1f0db2800d13b6c2b120e05129cd13cb">statevec_rotateY</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>, angle);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  }</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <a class="code" href="QuEST__qasm_8c.html#aabeb3e9ec6b2f30938c4cf9592e624fa">qasm_recordParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fae1267d5de573dc2901aa8e724ac1d689">GATE_ROTATE_Y</a>, targetQubit, angle);</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00028">GATE_ROTATE_Y</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00187">qasm_recordParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00302">statevec_rotateY()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02414">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gab23a8b022ec83b9d423961ca87cd8cb5"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gab23a8b022ec83b9d423961ca87cd8cb5">◆ </a></span>rotateZ()</h2>
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<td class="memname">void rotateZ </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>rotQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="group__type.html#ga7740e349b4f8bae6451547680f0ce2d6">qreal</a> </td>
<td class="paramname"><em>angle</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Rotate a single qubit by a given angle around the Z-axis of the Bloch-sphere (also known as a phase shift gate). </p>
<p><br />
For angle <img class="formulaInl" alt="$\theta$" src="form_64.png"/>, applies </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} \exp(-i \theta/2) & 0 \\ 0 & \exp(i \theta/2) \end{pmatrix} \]" src="form_99.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {rot}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {$R_z(\theta)$}; \end{tikzpicture} \]" src="form_100.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga3250d0d95b5d755cad542a6a2372b894" title="Apply a multi-qubit Z rotation, also known as a phase gadget, on a selected number of qubits.">multiRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga7eb969c1dd6c949aecf716d2fba71120" title="Applies a controlled rotation by a given angle around the Z-axis of the Bloch-sphere.">controlledRotateZ()</a></li>
<li><a class="el" href="group__unitary.html#ga34312ff52cc28bcab3cbd2ff338fd081" title="Rotate a single qubit by a given angle around the Y-axis of the Bloch-sphere.">rotateY()</a></li>
<li><a class="el" href="group__unitary.html#ga8886a3793b21622c48cf3bad6e15082d" title="Rotate a single qubit by a given angle around the X-axis of the Bloch-sphere.">rotateX()</a></li>
<li><a class="el" href="group__unitary.html#ga4c708f066b244801e10f538b48b90145" title="Rotate a single qubit by a given angle around a given Vector on the Bloch-sphere.">rotateAroundAxis()</a></li>
<li><a class="el" href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5" title="Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...">multiRotatePauli()</a></li>
<li><a class="el" href="group__unitary.html#ga26baa057f5db8804825c2d611386753b" title="Shift the phase between and of a single qubit by a given angle.">phaseShift()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">rotQubit</td><td>qubit to rotate </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">angle</td><td>angle by which to rotate in radians </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>rotQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00209">209</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  {</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <a class="code" href="QuEST__common_8c.html#a2b2b8c69566a49cdf4a3fa2cb4f5e03c">statevec_rotateZ</a>(qureg, targetQubit, angle);</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <a class="code" href="QuEST__common_8c.html#a2b2b8c69566a49cdf4a3fa2cb4f5e03c">statevec_rotateZ</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>, -angle);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  }</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  </div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <a class="code" href="QuEST__qasm_8c.html#aabeb3e9ec6b2f30938c4cf9592e624fa">qasm_recordParamGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa0cdc4c588d02a515a68515dd3f24d877">GATE_ROTATE_Z</a>, targetQubit, angle);</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00029">GATE_ROTATE_Z</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00187">qasm_recordParamGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00308">statevec_rotateZ()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02454">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga655ffcd4def2e127341c9488f5ca8455">◆ </a></span>sGate()</h2>
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<td class="memname">void sGate </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
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<td></td>
<td>)</td>
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<p>Apply the single-qubit S gate. </p>
<p>This is a rotation of <img class="formulaInl" alt="$\pi/2$" src="form_77.png"/> around the Z-axis on the Bloch sphere, or the unitary: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix} \]" src="form_78.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {S}; \end{tikzpicture} \]" src="form_79.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#gac15907193da5a7c48b9610a26e669064" title="Apply the single-qubit T gate.">tGate()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate upon </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00465">465</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  {</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  </div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <a class="code" href="QuEST__common_8c.html#a559d175d31cec552fc09aec3e8a78d11">statevec_sGate</a>(qureg, targetQubit);</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  <a class="code" href="QuEST__common_8c.html#a142b424d903dfaca7a7ac166076f543a">statevec_sGateConj</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>);</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  }</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  </div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  <a class="code" href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa5053f3d968443bc04e8b1d09f18bab9a">GATE_S</a>, targetQubit);</div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00025">GATE_S</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00179">qasm_recordGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00268">statevec_sGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00282">statevec_sGateConj()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02494">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga75d5e65f87c68403602a669b9c6d52b0">◆ </a></span>sqrtSwapGate()</h2>
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<td class="memname">void sqrtSwapGate </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>qb1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>qb2</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Performs a sqrt SWAP gate between <code>qubit1</code> and <code>qubit2</code>. </p>
<p>This effects </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & \frac{1}{2}(1+i) & \frac{1}{2}(1-i) \\\ & \frac{1}{2}(1-i) & \frac{1}{2}(1+i) \\ & & & 1 \end{pmatrix} \]" src="form_178.png"/>
</p>
<p> on the designated qubits, though is performed internally by three CNOT gates.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {qubit1}; \node[draw=none] at (-3.5, 0) {qubit2}; \draw (-2, 2) -- (2, 2); \draw (0, 2) -- (0, 0); \draw (-2,0) -- (2, 0); \draw (-.35,-.35) -- (.35,.35); \draw (-.35,.35) -- (.35,-.35); \draw (-.35,-.35 + 2) -- (.35,.35 + 2); \draw (-.35,.35 + 2) -- (.35,-.35 + 2); \draw[fill=white] (0, 1) circle (.5); \node[draw=none] at (0, 1) {1/2}; \end{tikzpicture} \]" src="form_179.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga820fd139c035136819e371308c206e36" title="Performs a SWAP gate between qubit1 and qubit2.">swapGate()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">qb1</td><td>qubit to sqrt swap </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">qb2</td><td>other qubit to sqrt swap </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>qubit1</code> or <code>qubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>qubit1</code> and <code>qubit2</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00639">639</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00639"></a><span class="lineno"> 639</span>  {</div>
<div class="line"><a name="l00640"></a><span class="lineno"> 640</span>  <a class="code" href="QuEST__validation_8c.html#aed5f85789dc4fa43b64e99e6b538035c">validateUniqueTargets</a>(qureg, qb1, qb2, __func__);</div>
<div class="line"><a name="l00641"></a><span class="lineno"> 641</span>  <a class="code" href="QuEST__validation_8c.html#aa28b7d9c0c3cf9c4be0e324fb9d6bf76">validateMultiQubitMatrixFitsInNode</a>(qureg, 2, __func__); <span class="comment">// uses 2qb unitary in QuEST_common</span></div>
<div class="line"><a name="l00642"></a><span class="lineno"> 642</span>  </div>
<div class="line"><a name="l00643"></a><span class="lineno"> 643</span>  <a class="code" href="QuEST__common_8c.html#a6550462400942be61b171c8840b36aa1">statevec_sqrtSwapGate</a>(qureg, qb1, qb2);</div>
<div class="line"><a name="l00644"></a><span class="lineno"> 644</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00645"></a><span class="lineno"> 645</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00646"></a><span class="lineno"> 646</span>  <a class="code" href="QuEST__common_8c.html#a33cde9b6518d55a544eff20301a5d844">statevec_sqrtSwapGateConj</a>(qureg, qb1+shift, qb2+shift);</div>
<div class="line"><a name="l00647"></a><span class="lineno"> 647</span>  }</div>
<div class="line"><a name="l00648"></a><span class="lineno"> 648</span>  </div>
<div class="line"><a name="l00649"></a><span class="lineno"> 649</span>  <a class="code" href="QuEST__qasm_8c.html#aa4c380db9eda18892d5a86825fa4b165">qasm_recordControlledGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fab656861dfb036cbcf7009f02a8949253">GATE_SQRT_SWAP</a>, qb1, qb2);</div>
<div class="line"><a name="l00650"></a><span class="lineno"> 650</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00034">GATE_SQRT_SWAP</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00239">qasm_recordControlledGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00387">statevec_sqrtSwapGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00400">statevec_sqrtSwapGateConj()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00473">validateMultiQubitMatrixFitsInNode()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00414">validateUniqueTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02533">TEST_CASE()</a>.</p>
</div>
</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ga820fd139c035136819e371308c206e36">◆ </a></span>swapGate()</h2>
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<td class="memname">void swapGate </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>qubit1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>qubit2</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>Performs a SWAP gate between <code>qubit1</code> and <code>qubit2</code>. </p>
<p>This effects </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 \\ & & 1 \\\ & 1 \\ & & & 1 \end{pmatrix} \]" src="form_176.png"/>
</p>
<p> on the designated qubits, though is performed internally by three CNOT gates.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 2) {qubit1}; \node[draw=none] at (-3.5, 0) {qubit2}; \draw (-2, 2) -- (2, 2); \draw (0, 2) -- (0, 0); \draw (-2,0) -- (2, 0); \draw (-.35,-.35) -- (.35,.35); \draw (-.35,.35) -- (.35,-.35); \draw (-.35,-.35 + 2) -- (.35,.35 + 2); \draw (-.35,.35 + 2) -- (.35,-.35 + 2); \end{tikzpicture} \]" src="form_177.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga75d5e65f87c68403602a669b9c6d52b0" title="Performs a sqrt SWAP gate between qubit1 and qubit2.">sqrtSwapGate()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">qubit1</td><td>qubit to swap </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">qubit2</td><td>other qubit to swap </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if either <code>qubit1</code> or <code>qubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>qubit1</code> and <code>qubit2</code> are equal </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00627">627</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00627"></a><span class="lineno"> 627</span>  {</div>
<div class="line"><a name="l00628"></a><span class="lineno"> 628</span>  <a class="code" href="QuEST__validation_8c.html#aed5f85789dc4fa43b64e99e6b538035c">validateUniqueTargets</a>(qureg, qb1, qb2, __func__);</div>
<div class="line"><a name="l00629"></a><span class="lineno"> 629</span>  </div>
<div class="line"><a name="l00630"></a><span class="lineno"> 630</span>  <a class="code" href="QuEST__internal_8h.html#ab7478fcaf6357ab202d72853b672e375">statevec_swapQubitAmps</a>(qureg, qb1, qb2);</div>
<div class="line"><a name="l00631"></a><span class="lineno"> 631</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00632"></a><span class="lineno"> 632</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00633"></a><span class="lineno"> 633</span>  <a class="code" href="QuEST__internal_8h.html#ab7478fcaf6357ab202d72853b672e375">statevec_swapQubitAmps</a>(qureg, qb1+shift, qb2+shift);</div>
<div class="line"><a name="l00634"></a><span class="lineno"> 634</span>  }</div>
<div class="line"><a name="l00635"></a><span class="lineno"> 635</span>  </div>
<div class="line"><a name="l00636"></a><span class="lineno"> 636</span>  <a class="code" href="QuEST__qasm_8c.html#aa4c380db9eda18892d5a86825fa4b165">qasm_recordControlledGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fab12d052de2b7c59c6ab87710fd7d3c78">GATE_SWAP</a>, qb1, qb2);</div>
<div class="line"><a name="l00637"></a><span class="lineno"> 637</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00033">GATE_SWAP</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00239">qasm_recordControlledGate()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l01431">statevec_swapQubitAmps()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00414">validateUniqueTargets()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02583">TEST_CASE()</a>.</p>
</div>
</div>
<a id="gac15907193da5a7c48b9610a26e669064"></a>
<h2 class="memtitle"><span class="permalink"><a href="#gac15907193da5a7c48b9610a26e669064">◆ </a></span>tGate()</h2>
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<td class="memname">void tGate </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
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</div><div class="memdoc">
<p>Apply the single-qubit T gate. </p>
<p>This is a rotation of <img class="formulaInl" alt="$\pi/4$" src="form_80.png"/> around the Z-axis on the Bloch sphere, or the unitary: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} 1 & 0 \\ 0 & \exp\left(i \frac{\pi}{4}\right) \end{pmatrix} \]" src="form_81.png"/>
</p>
<p> with circuit diagram: </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {T}; \end{tikzpicture} \]" src="form_82.png"/>
</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="group__unitary.html#ga655ffcd4def2e127341c9488f5ca8455" title="Apply the single-qubit S gate.">sGate()</a></li>
</ul>
</dd></dl>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate upon </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>) </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00476">476</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  {</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  </div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <a class="code" href="QuEST__common_8c.html#a2d96b4601cc3a9e1221e11a366fe1699">statevec_tGate</a>(qureg, targetQubit);</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  <a class="code" href="QuEST__common_8c.html#a086fffa88b1aeec1405aa2dc41eab8a3">statevec_tGateConj</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>);</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  }</div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  </div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  <a class="code" href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a>(qureg, <a class="code" href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fadfa058950331ffdba0bf56cb2272e01f">GATE_T</a>, targetQubit);</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__qasm_8h_source.html#l00024">GATE_T</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00179">qasm_recordGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00275">statevec_tGate()</a>, <a class="el" href="QuEST__common_8c_source.html#l00289">statevec_tGateConj()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02631">TEST_CASE()</a>.</p>
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</div>
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<h2 class="memtitle"><span class="permalink"><a href="#gab525a42d63233f61afeb6be97d89dd36">◆ </a></span>twoQubitUnitary()</h2>
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<td class="memname">void twoQubitUnitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit1</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit2</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix4.html">ComplexMatrix4</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
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<p>Apply a general two-qubit unitary (including a global phase factor). </p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target2}; \node[draw=none] at (-3.5, 2) {target1}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-2,2) -- (-1, 2); \draw (1, 2) -- (2, 2); \draw (-1,-1)--(-1,3)--(1,3)--(1,-1)--cycle; \node[draw=none] at (0, 1) {U}; \end{tikzpicture} \]" src="form_210.png"/>
</p>
<p><code>targetQubit1</code> is treated as the <code>least</code> significant qubit in <code>u</code>, such that a row in <code>u</code> is dotted with the vector <img class="formulaInl" alt="$ |\text{targetQubit2} \;\; \text{targetQubit1}\rangle : \{ |00\rangle, |01\rangle, |10\rangle, |11\rangle \} $" src="form_211.png"/></p>
<p>For example, </p><div class="fragment"><div class="line"><a class="code" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36">twoQubitUnitary</a>(qureg, a, b, u);</div>
</div><!-- fragment --><p>will invoke multiplication </p><p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{pmatrix} u_{00} & u_{01} & u_{02} & u_{03} \\ u_{10} & u_{11} & u_{12} & u_{13} \\ u_{20} & u_{21} & u_{22} & u_{23} \\ u_{30} & u_{31} & u_{32} & u_{33} \end{pmatrix} \begin{pmatrix} |ba\rangle = |00\rangle \\ |ba\rangle = |01\rangle \\ |ba\rangle = |10\rangle \\ |ba\rangle = |11\rangle \end{pmatrix} \]" src="form_212.png"/>
</p>
<p>The passed <a class="el" href="structComplexMatrix4.html" title="Represents a 4x4 matrix of complex numbers.">ComplexMatrix4</a> must be unitary, otherwise an error is thrown. </p><blockquote class="doxtable">
<p>Use <a class="el" href="group__operator.html#ga74a955ec4bce606d89317bcfc528387f" title="Apply a general 4-by-4 matrix, which may be non-unitary.">applyMatrix4()</a> to left-multiply a non-unitary <a class="el" href="structComplexMatrix4.html" title="Represents a 4x4 matrix of complex numbers.">ComplexMatrix4</a>. </p>
</blockquote>
<p>Note that in distributed mode, this routine requires that each node contains at least 4 amplitudes. This means an q-qubit register (state vector or density matrix) can be distributed by at most 2^q/4 nodes.</p>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix4.html" title="Represents a 4x4 matrix of complex numbers.">ComplexMatrix4</a></li>
<li><a class="el" href="group__unitary.html#ga3d89916b46bc4aaf23e938022e6c89c1" title="Apply a general controlled two-qubit unitary (including a global phase factor).">controlledTwoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga65c7879947e398690a5428bd43e143e3" title="Apply a general multi-controlled two-qubit unitary (including a global phase factor).">multiControlledTwoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
<li><a class="el" href="group__operator.html#ga74a955ec4bce606d89317bcfc528387f" title="Apply a general 4-by-4 matrix, which may be non-unitary.">applyMatrix4()</a></li>
</ul>
</dd></dl>
<p><br />
</p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit1</td><td>first qubit to operate on, treated as least significant in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit2</td><td>second qubit to operate on, treated as most significant in <code>u</code> </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit1</code> or <code>targetQubit2</code> are outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if <code>targetQubit1</code> equals <code>targetQubit2</code> </li>
<li>if matrix <code>u</code> is not unitary</li>
<li>if each node cannot fit 4 amplitudes in distributed mode </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Tyson Jones </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00256">256</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  {</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <a class="code" href="QuEST__validation_8c.html#a6776217a5f7ba38b56175cf6db0f96e0">validateMultiTargets</a>(qureg, (<span class="keywordtype">int</span> []) {targetQubit1, targetQubit2}, 2, __func__);</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <a class="code" href="QuEST__validation_8c.html#a654db9d60abdcae26427e7d3b3d9c432">validateTwoQubitUnitaryMatrix</a>(qureg, u, __func__);</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  </div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <a class="code" href="QuEST__common_8c.html#a95abbe0cedf45b1ff2f070dba219fd7f">statevec_twoQubitUnitary</a>(qureg, targetQubit1, targetQubit2, u);</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordtype">int</span> shift = qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <a class="code" href="QuEST__common_8c.html#a95abbe0cedf45b1ff2f070dba219fd7f">statevec_twoQubitUnitary</a>(qureg, targetQubit1+shift, targetQubit2+shift, <a class="code" href="QuEST__common_8c.html#a20d45e85dd49dd3bf6045990b590b24b">getConjugateMatrix4</a>(u));</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  }</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <a class="code" href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a>(qureg, <span class="stringliteral">"Here, an undisclosed 2-qubit unitary was applied."</span>);</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00110">getConjugateMatrix4()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00121">qasm_recordComment()</a>, <a class="el" href="QuEST__common_8c_source.html#l00561">statevec_twoQubitUnitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00428">validateMultiTargets()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00481">validateTwoQubitUnitaryMatrix()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02670">TEST_CASE()</a>.</p>
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<h2 class="memtitle"><span class="permalink"><a href="#ga78b814256f851cac70fdf3cbf9cfc206">◆ </a></span>unitary()</h2>
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<td class="memname">void unitary </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structQureg.html">Qureg</a> </td>
<td class="paramname"><em>qureg</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int </td>
<td class="paramname"><em>targetQubit</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structComplexMatrix2.html">ComplexMatrix2</a> </td>
<td class="paramname"><em>u</em> </td>
</tr>
<tr>
<td></td>
<td>)</td>
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<p>Apply a general single-qubit unitary (including a global phase factor). </p>
<p>The passed 2x2 ComplexMatrix must be unitary, otherwise an error is thrown.</p>
<p class="formulaDsp">
<img class="formulaDsp" alt="\[ \begin{tikzpicture}[scale=.5] \node[draw=none] at (-3.5, 0) {target}; \draw (-2,0) -- (-1, 0); \draw (1, 0) -- (2, 0); \draw (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle; \node[draw=none] at (0, 0) {U}; \end{tikzpicture} \]" src="form_92.png"/>
</p>
<p>If <code>qureg</code> is a state-vector, then the resulting state is <img class="formulaInl" alt="$ u \, |\text{qureg}\rangle $" src="form_93.png"/>.<br />
If <code>qureg</code> is a density-matrix <img class="formulaInl" alt="$ \rho $" src="form_47.png"/>, then the resulting state is <img class="formulaInl" alt="$ u \, \rho \, u^\dagger $" src="form_94.png"/>.</p>
<blockquote class="doxtable">
<p>Use <a class="el" href="group__operator.html#gadfb5c1d99a22ce666fc715a8da2e0950" title="Apply a general 2-by-2 matrix, which may be non-unitary.">applyMatrix2()</a> to left-multiply a non-unitary <a class="el" href="structComplexMatrix2.html" title="Represents a 2x2 matrix of complex numbers.">ComplexMatrix2</a> </p>
</blockquote>
<dl class="section see"><dt>See also</dt><dd><ul>
<li><a class="el" href="structComplexMatrix2.html" title="Represents a 2x2 matrix of complex numbers.">ComplexMatrix2</a></li>
<li><a class="el" href="group__unitary.html#gaa3fb996a5cadd098f4acd8aec955cf9c" title="Apply a general controlled unitary (single control, single target), which can include a global phase ...">controlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gaa700dc9657ade4cf16f1cad1624c5332" title="Apply a general multiple-control single-target unitary, which can include a global phase factor.">multiControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga41b946a82982c3fa3dc2a7395665bc90" title="Apply a general single-qubit unitary with multiple control qubits, conditioned upon a specific bit se...">multiStateControlledUnitary()</a></li>
<li><a class="el" href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36" title="Apply a general two-qubit unitary (including a global phase factor).">twoQubitUnitary()</a></li>
<li><a class="el" href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f" title="Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...">multiQubitUnitary()</a></li>
<li><a class="el" href="group__operator.html#gadfb5c1d99a22ce666fc715a8da2e0950" title="Apply a general 2-by-2 matrix, which may be non-unitary.">applyMatrix2()</a></li>
<li><a class="el" href="group__unitary.html#gaefaa7acba90373efe4e0f0b94987c734" title="Apply a single-qubit unitary parameterised by two given complex scalars.">compactUnitary()</a></li>
</ul>
</dd></dl>
<p><br />
</p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in,out]</td><td class="paramname">qureg</td><td>object representing the set of all qubits </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">targetQubit</td><td>qubit to operate on </td></tr>
<tr><td class="paramdir">[in]</td><td class="paramname">u</td><td>unitary matrix to apply </td></tr>
</table>
</dd>
</dl>
<dl class="exception"><dt>Exceptions</dt><dd>
<table class="exception">
<tr><td class="paramname"><a class="el" href="group__debug.html#ga51a64b05d31ef9bcf6a63ce26c0092db" title="An internal function called when invalid arguments are passed to a QuEST API call,...">invalidQuESTInputError()</a></td><td><ul>
<li>if <code>targetQubit</code> is outside [0, <code>qureg.numQubitsRepresented</code>)</li>
<li>if matrix <code>u</code> is not unitary </li>
</ul>
</td></tr>
</table>
</dd>
</dl>
<dl class="section author"><dt>Author</dt><dd>Ania Brown (state-vector) </dd>
<dd>
Tyson Jones (density matrix, doc) </dd></dl>
<p class="definition">Definition at line <a class="el" href="QuEST_8c_source.html#l00348">348</a> of file <a class="el" href="QuEST_8c_source.html">QuEST.c</a>.</p>
<div class="fragment"><div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  {</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <a class="code" href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a>(qureg, targetQubit, __func__);</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <a class="code" href="QuEST__validation_8c.html#a0344fbbb2bb505f7db14b420153f1eb5">validateOneQubitUnitaryMatrix</a>(u, __func__);</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  </div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  <a class="code" href="QuEST__internal_8h.html#ac3735bd959600e57b2ee3a105666cddf">statevec_unitary</a>(qureg, targetQubit, u);</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  <span class="keywordflow">if</span> (qureg.<a class="code" href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">isDensityMatrix</a>) {</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <a class="code" href="QuEST__internal_8h.html#ac3735bd959600e57b2ee3a105666cddf">statevec_unitary</a>(qureg, targetQubit+qureg.<a class="code" href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">numQubitsRepresented</a>, <a class="code" href="QuEST__common_8c.html#ad34d98eeaa6a3cb45e92c696cfd2d1c8">getConjugateMatrix2</a>(u));</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  }</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  <a class="code" href="QuEST__qasm_8c.html#ad22260712869e79f07d2f04e2b41a233">qasm_recordUnitary</a>(qureg, u, targetQubit);</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span> }</div>
</div><!-- fragment -->
<p class="reference">References <a class="el" href="QuEST__common_8c_source.html#l00105">getConjugateMatrix2()</a>, <a class="el" href="QuEST_8h_source.html#l00325">Qureg::isDensityMatrix</a>, <a class="el" href="QuEST_8h_source.html#l00327">Qureg::numQubitsRepresented</a>, <a class="el" href="QuEST__qasm_8c_source.html#l00208">qasm_recordUnitary()</a>, <a class="el" href="QuEST__cpu__distributed_8c_source.html#l00895">statevec_unitary()</a>, <a class="el" href="QuEST__validation_8c_source.html#l00477">validateOneQubitUnitaryMatrix()</a>, and <a class="el" href="QuEST__validation_8c_source.html#l00400">validateTarget()</a>.</p>
<p class="reference">Referenced by <a class="el" href="test__unitaries_8cpp_source.html#l02735">TEST_CASE()</a>.</p>
</div>
</div>
</div><!-- contents -->
<div class="ttc" id="aQuEST__common_8c_html_a5ef139196852f92fe8271c82964eadff"><div class="ttname"><a href="QuEST__common_8c.html#a5ef139196852f92fe8271c82964eadff">statevec_phaseShift</a></div><div class="ttdeci">void statevec_phaseShift(Qureg qureg, int targetQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00254">QuEST_common.c:254</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a97f43ad2fe1ffc1f77a9b2af2f5f1cc2"><div class="ttname"><a href="QuEST__validation_8c.html#a97f43ad2fe1ffc1f77a9b2af2f5f1cc2">validateMultiControlsTarget</a></div><div class="ttdeci">void validateMultiControlsTarget(Qureg qureg, int *controlQubits, int numControlQubits, int targetQubit, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00452">QuEST_validation.c:452</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a559d175d31cec552fc09aec3e8a78d11"><div class="ttname"><a href="QuEST__common_8c.html#a559d175d31cec552fc09aec3e8a78d11">statevec_sGate</a></div><div class="ttdeci">void statevec_sGate(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00268">QuEST_common.c:268</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_ab14df201e5c05527dc77cfeb6f583042"><div class="ttname"><a href="QuEST__common_8c.html#ab14df201e5c05527dc77cfeb6f583042">statevec_pauliZ</a></div><div class="ttdeci">void statevec_pauliZ(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00261">QuEST_common.c:261</a></div></div>
<div class="ttc" id="agroup__type_html_ga1c703cf89629e4e9c7023cd402d67028"><div class="ttname"><a href="group__type.html#ga1c703cf89629e4e9c7023cd402d67028">pauliOpType</a></div><div class="ttdeci">pauliOpType</div><div class="ttdoc">Codes for specifying Pauli operators.</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00096">QuEST.h:96</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_ab8687e6ea5cf35503c223051837f3b94"><div class="ttname"><a href="QuEST__common_8c.html#ab8687e6ea5cf35503c223051837f3b94">statevec_rotateX</a></div><div class="ttdeci">void statevec_rotateX(Qureg qureg, int rotQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00296">QuEST_common.c:296</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_ac31c45c5a31c523be0eb26abba6cf598"><div class="ttname"><a href="QuEST__validation_8c.html#ac31c45c5a31c523be0eb26abba6cf598">validateTarget</a></div><div class="ttdeci">void validateTarget(Qureg qureg, int targetQubit, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00400">QuEST_validation.c:400</a></div></div>
<div class="ttc" id="agroup__unitary_html_gab525a42d63233f61afeb6be97d89dd36"><div class="ttname"><a href="group__unitary.html#gab525a42d63233f61afeb6be97d89dd36">twoQubitUnitary</a></div><div class="ttdeci">void twoQubitUnitary(Qureg qureg, int targetQubit1, int targetQubit2, ComplexMatrix4 u)</div><div class="ttdoc">Apply a general two-qubit unitary (including a global phase factor).</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8c_source.html#l00256">QuEST.c:256</a></div></div>
<div class="ttc" id="agroup__type_html_gga1c703cf89629e4e9c7023cd402d67028a085c85cff6ba79c52d8b1e61c42ddddf"><div class="ttname"><a href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a085c85cff6ba79c52d8b1e61c42ddddf">PAULI_Z</a></div><div class="ttdeci">@ PAULI_Z</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00096">QuEST.h:96</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a08d2e22870f3ef0289e355d634ea17a2"><div class="ttname"><a href="QuEST__common_8c.html#a08d2e22870f3ef0289e355d634ea17a2">statevec_multiControlledMultiRotatePauli</a></div><div class="ttdeci">void statevec_multiControlledMultiRotatePauli(Qureg qureg, long long int ctrlMask, int *targetQubits, enum pauliOpType *targetPaulis, int numTargets, qreal angle, int applyConj)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00453">QuEST_common.c:453</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_aabeb3e9ec6b2f30938c4cf9592e624fa"><div class="ttname"><a href="QuEST__qasm_8c.html#aabeb3e9ec6b2f30938c4cf9592e624fa">qasm_recordParamGate</a></div><div class="ttdeci">void qasm_recordParamGate(Qureg qureg, TargetGate gate, int targetQubit, qreal param)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00187">QuEST_qasm.c:187</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_acf1c651a4359a370a2d9b3e1e1ebd430"><div class="ttname"><a href="QuEST__common_8c.html#acf1c651a4359a370a2d9b3e1e1ebd430">shiftIndices</a></div><div class="ttdeci">void shiftIndices(int *indices, int numIndices, int shift)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00156">QuEST_common.c:156</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_ad7ac4934371d72e24c6d1cea3d3da391"><div class="ttname"><a href="QuEST__common_8c.html#ad7ac4934371d72e24c6d1cea3d3da391">statevec_controlledTwoQubitUnitary</a></div><div class="ttdeci">void statevec_controlledTwoQubitUnitary(Qureg qureg, int controlQubit, int targetQubit1, int targetQubit2, ComplexMatrix4 u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00567">QuEST_common.c:567</a></div></div>
<div class="ttc" id="agroup__type_html_gga1c703cf89629e4e9c7023cd402d67028a63800f45b01ccc2608f754aee850bf4a"><div class="ttname"><a href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a63800f45b01ccc2608f754aee850bf4a">PAULI_I</a></div><div class="ttdeci">@ PAULI_I</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00096">QuEST.h:96</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fadfa058950331ffdba0bf56cb2272e01f"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fadfa058950331ffdba0bf56cb2272e01f">GATE_T</a></div><div class="ttdeci">@ GATE_T</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00024">QuEST_qasm.h:24</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fa4668b36d21aaeba1fb605b73881ca507"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa4668b36d21aaeba1fb605b73881ca507">GATE_PHASE_SHIFT</a></div><div class="ttdeci">@ GATE_PHASE_SHIFT</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00032">QuEST_qasm.h:32</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_ad22260712869e79f07d2f04e2b41a233"><div class="ttname"><a href="QuEST__qasm_8c.html#ad22260712869e79f07d2f04e2b41a233">qasm_recordUnitary</a></div><div class="ttdeci">void qasm_recordUnitary(Qureg qureg, ComplexMatrix2 u, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00208">QuEST_qasm.c:208</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_abecd71c919a35e5a87b07ba400edc7c2"><div class="ttname"><a href="QuEST__qasm_8c.html#abecd71c919a35e5a87b07ba400edc7c2">qasm_recordMultiControlledGate</a></div><div class="ttdeci">void qasm_recordMultiControlledGate(Qureg qureg, TargetGate gate, int *controlQubits, int numControlQubits, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00317">QuEST_qasm.c:317</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_aa28b7d9c0c3cf9c4be0e324fb9d6bf76"><div class="ttname"><a href="QuEST__validation_8c.html#aa28b7d9c0c3cf9c4be0e324fb9d6bf76">validateMultiQubitMatrixFitsInNode</a></div><div class="ttdeci">void validateMultiQubitMatrixFitsInNode(Qureg qureg, int numTargets, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00473">QuEST_validation.c:473</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a95abbe0cedf45b1ff2f070dba219fd7f"><div class="ttname"><a href="QuEST__common_8c.html#a95abbe0cedf45b1ff2f070dba219fd7f">statevec_twoQubitUnitary</a></div><div class="ttdeci">void statevec_twoQubitUnitary(Qureg qureg, int targetQubit1, int targetQubit2, ComplexMatrix4 u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00561">QuEST_common.c:561</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a086fffa88b1aeec1405aa2dc41eab8a3"><div class="ttname"><a href="QuEST__common_8c.html#a086fffa88b1aeec1405aa2dc41eab8a3">statevec_tGateConj</a></div><div class="ttdeci">void statevec_tGateConj(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00289">QuEST_common.c:289</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_ac3735bd959600e57b2ee3a105666cddf"><div class="ttname"><a href="QuEST__internal_8h.html#ac3735bd959600e57b2ee3a105666cddf">statevec_unitary</a></div><div class="ttdeci">void statevec_unitary(Qureg qureg, int targetQubit, ComplexMatrix2 u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l00895">QuEST_cpu_distributed.c:895</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a20d45e85dd49dd3bf6045990b590b24b"><div class="ttname"><a href="QuEST__common_8c.html#a20d45e85dd49dd3bf6045990b590b24b">getConjugateMatrix4</a></div><div class="ttdeci">ComplexMatrix4 getConjugateMatrix4(ComplexMatrix4 src)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00110">QuEST_common.c:110</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fada07505b73935b2788032efd30a1a361"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fada07505b73935b2788032efd30a1a361">GATE_ROTATE_X</a></div><div class="ttdeci">@ GATE_ROTATE_X</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00027">QuEST_qasm.h:27</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_ab9947ff071a0c019f715f04b3833dcfd"><div class="ttname"><a href="QuEST__validation_8c.html#ab9947ff071a0c019f715f04b3833dcfd">validateMultiQubitUnitaryMatrix</a></div><div class="ttdeci">void validateMultiQubitUnitaryMatrix(Qureg qureg, ComplexMatrixN u, int numTargs, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00502">QuEST_validation.c:502</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a0acfe30083d0bc2a84da196378a36122"><div class="ttname"><a href="QuEST__internal_8h.html#a0acfe30083d0bc2a84da196378a36122">statevec_multiControlledMultiQubitUnitary</a></div><div class="ttdeci">void statevec_multiControlledMultiQubitUnitary(Qureg qureg, long long int ctrlMask, int *targs, int numTargs, ComplexMatrixN u)</div><div class="ttdoc">This calls swapQubitAmps only when it would involve a distributed communication; if the qubit chunks ...</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01514">QuEST_cpu_distributed.c:1514</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a8d88b4ed94ab024e5e7b2f1f4f505b44"><div class="ttname"><a href="QuEST__internal_8h.html#a8d88b4ed94ab024e5e7b2f1f4f505b44">statevec_multiRotateZ</a></div><div class="ttdeci">void statevec_multiRotateZ(Qureg qureg, long long int mask, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu_8c_source.html#l03316">QuEST_cpu.c:3316</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a6bd68fa9c0c1bd9c9f9af714ea0b8b03"><div class="ttname"><a href="QuEST__qasm_8c.html#a6bd68fa9c0c1bd9c9f9af714ea0b8b03">qasm_recordControlledCompactUnitary</a></div><div class="ttdeci">void qasm_recordControlledCompactUnitary(Qureg qureg, Complex alpha, Complex beta, int controlQubit, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00265">QuEST_qasm.c:265</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fa0cdc4c588d02a515a68515dd3f24d877"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa0cdc4c588d02a515a68515dd3f24d877">GATE_ROTATE_Z</a></div><div class="ttdeci">@ GATE_ROTATE_Z</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00029">QuEST_qasm.h:29</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fa228cd6a7ad18928b794ee7ad1f1fc85e"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa228cd6a7ad18928b794ee7ad1f1fc85e">GATE_SIGMA_Z</a></div><div class="ttdeci">@ GATE_SIGMA_Z</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00023">QuEST_qasm.h:23</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a4e19ef93d01d7acea32ca646d623aedd"><div class="ttname"><a href="QuEST__internal_8h.html#a4e19ef93d01d7acea32ca646d623aedd">statevec_controlledPauliY</a></div><div class="ttdeci">void statevec_controlledPauliY(Qureg qureg, int controlQubit, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01192">QuEST_cpu_distributed.c:1192</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_af92fa737f4491324408b3d15543dced4"><div class="ttname"><a href="QuEST__common_8c.html#af92fa737f4491324408b3d15543dced4">getConjugateScalar</a></div><div class="ttdeci">Complex getConjugateScalar(Complex scalar)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00091">QuEST_common.c:91</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a63df1ec14ff7cc81c3f392ac10fcc744"><div class="ttname"><a href="QuEST__internal_8h.html#a63df1ec14ff7cc81c3f392ac10fcc744">statevec_controlledPhaseShift</a></div><div class="ttdeci">void statevec_controlledPhaseShift(Qureg qureg, int idQubit1, int idQubit2, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu_8c_source.html#l03226">QuEST_cpu.c:3226</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fa8417e56d80add49216437e0d451e8dd9"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa8417e56d80add49216437e0d451e8dd9">GATE_HADAMARD</a></div><div class="ttdeci">@ GATE_HADAMARD</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00026">QuEST_qasm.h:26</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_ad34d98eeaa6a3cb45e92c696cfd2d1c8"><div class="ttname"><a href="QuEST__common_8c.html#ad34d98eeaa6a3cb45e92c696cfd2d1c8">getConjugateMatrix2</a></div><div class="ttdeci">ComplexMatrix2 getConjugateMatrix2(ComplexMatrix2 src)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00105">QuEST_common.c:105</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_aa662796ea6e0f471143c53becae8c12c"><div class="ttname"><a href="QuEST__internal_8h.html#aa662796ea6e0f471143c53becae8c12c">statevec_multiControlledPhaseShift</a></div><div class="ttdeci">void statevec_multiControlledPhaseShift(Qureg qureg, int *controlQubits, int numControlQubits, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu_8c_source.html#l03266">QuEST_cpu.c:3266</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_af1cca787f3b0e0c91ffb2495f9ad8d5a"><div class="ttname"><a href="QuEST__internal_8h.html#af1cca787f3b0e0c91ffb2495f9ad8d5a">statevec_pauliY</a></div><div class="ttdeci">void statevec_pauliY(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01142">QuEST_cpu_distributed.c:1142</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a2275a3f14e8853261533ee41416ae19d"><div class="ttname"><a href="QuEST__qasm_8c.html#a2275a3f14e8853261533ee41416ae19d">qasm_recordMultiControlledMultiQubitNot</a></div><div class="ttdeci">void qasm_recordMultiControlledMultiQubitNot(Qureg qureg, int *ctrls, int numCtrls, int *targs, int numTargs)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00382">QuEST_qasm.c:382</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a06b8474aec51579ff680fb66439e7fc6"><div class="ttname"><a href="QuEST__common_8c.html#a06b8474aec51579ff680fb66439e7fc6">statevec_controlledMultiQubitUnitary</a></div><div class="ttdeci">void statevec_controlledMultiQubitUnitary(Qureg qureg, int ctrl, int *targets, int numTargets, ComplexMatrixN u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00579">QuEST_common.c:579</a></div></div>
<div class="ttc" id="agroup__unitary_html_ga34aa4865c92f9aa5d898c91286c9eca5"><div class="ttname"><a href="group__unitary.html#ga34aa4865c92f9aa5d898c91286c9eca5">multiRotatePauli</a></div><div class="ttdeci">void multiRotatePauli(Qureg qureg, int *targetQubits, enum pauliOpType *targetPaulis, int numTargets, qreal angle)</div><div class="ttdoc">Apply a multi-qubit multi-Pauli rotation, also known as a Pauli gadget, on a selected number of qubit...</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8c_source.html#l00685">QuEST.c:685</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a9975b6f54f4090cdf851958bc2b37230"><div class="ttname"><a href="QuEST__qasm_8c.html#a9975b6f54f4090cdf851958bc2b37230">qasm_recordMultiStateControlledUnitary</a></div><div class="ttdeci">void qasm_recordMultiStateControlledUnitary(Qureg qureg, ComplexMatrix2 u, int *controlQubits, int *controlState, int numControlQubits, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00363">QuEST_qasm.c:363</a></div></div>
<div class="ttc" id="agroup__unitary_html_ga20bf9b8a71b8a3ee4651e9497e6d1f4f"><div class="ttname"><a href="group__unitary.html#ga20bf9b8a71b8a3ee4651e9497e6d1f4f">multiQubitUnitary</a></div><div class="ttdeci">void multiQubitUnitary(Qureg qureg, int *targs, int numTargs, ComplexMatrixN u)</div><div class="ttdoc">Apply a general multi-qubit unitary (including a global phase factor) with any number of target qubit...</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8c_source.html#l00296">QuEST.c:296</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a6550462400942be61b171c8840b36aa1"><div class="ttname"><a href="QuEST__common_8c.html#a6550462400942be61b171c8840b36aa1">statevec_sqrtSwapGate</a></div><div class="ttdeci">void statevec_sqrtSwapGate(Qureg qureg, int qb1, int qb2)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00387">QuEST_common.c:387</a></div></div>
<div class="ttc" id="agroup__type_html_gga1c703cf89629e4e9c7023cd402d67028a7abac7bb5b71e17382014c443244ad5c"><div class="ttname"><a href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a7abac7bb5b71e17382014c443244ad5c">PAULI_X</a></div><div class="ttdeci">@ PAULI_X</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00096">QuEST.h:96</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_ab7478fcaf6357ab202d72853b672e375"><div class="ttname"><a href="QuEST__internal_8h.html#ab7478fcaf6357ab202d72853b672e375">statevec_swapQubitAmps</a></div><div class="ttdeci">void statevec_swapQubitAmps(Qureg qureg, int qb1, int qb2)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01431">QuEST_cpu_distributed.c:1431</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a4a2fa262d3f0dba372797b9bd35d9fa5"><div class="ttname"><a href="QuEST__internal_8h.html#a4a2fa262d3f0dba372797b9bd35d9fa5">statevec_controlledPauliYConj</a></div><div class="ttdeci">void statevec_controlledPauliYConj(Qureg qureg, int controlQubit, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01225">QuEST_cpu_distributed.c:1225</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a782c6f57939eeb72b7be8e247979f3be"><div class="ttname"><a href="QuEST__validation_8c.html#a782c6f57939eeb72b7be8e247979f3be">validateVector</a></div><div class="ttdeci">void validateVector(Vector vec, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00511">QuEST_validation.c:511</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a13ecc24b355a5213d745651cde56bd71"><div class="ttname"><a href="QuEST__internal_8h.html#a13ecc24b355a5213d745651cde56bd71">statevec_multiControlledMultiQubitNot</a></div><div class="ttdeci">void statevec_multiControlledMultiQubitNot(Qureg qureg, int ctrlMask, int targMask)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01097">QuEST_cpu_distributed.c:1097</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a9e7e85cfc36e3ce1f456a840a217bfd9"><div class="ttname"><a href="QuEST__validation_8c.html#a9e7e85cfc36e3ce1f456a840a217bfd9">validateMultiQubits</a></div><div class="ttdeci">void validateMultiQubits(Qureg qureg, int *qubits, int numQubits, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00444">QuEST_validation.c:444</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_add9ca9956cdd81ed5d0b0f66168c04a3"><div class="ttname"><a href="QuEST__internal_8h.html#add9ca9956cdd81ed5d0b0f66168c04a3">statevec_controlledUnitary</a></div><div class="ttdeci">void statevec_controlledUnitary(Qureg qureg, int controlQubit, int targetQubit, ComplexMatrix2 u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l00972">QuEST_cpu_distributed.c:972</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_aa4c380db9eda18892d5a86825fa4b165"><div class="ttname"><a href="QuEST__qasm_8c.html#aa4c380db9eda18892d5a86825fa4b165">qasm_recordControlledGate</a></div><div class="ttdeci">void qasm_recordControlledGate(Qureg qureg, TargetGate gate, int controlQubit, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00239">QuEST_qasm.c:239</a></div></div>
<div class="ttc" id="agroup__unitary_html_gab2ececaa253252e1b1cdb18a8452704a"><div class="ttname"><a href="group__unitary.html#gab2ececaa253252e1b1cdb18a8452704a">multiControlledMultiRotatePauli</a></div><div class="ttdeci">void multiControlledMultiRotatePauli(Qureg qureg, int *controlQubits, int numControls, int *targetQubits, enum pauliOpType *targetPaulis, int numTargets, qreal angle)</div><div class="ttdoc">Apply a multi-controlled multi-target multi-Pauli rotation, also known as a controlled Pauli gadget.</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8c_source.html#l00705">QuEST.c:705</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_aefc4a3a9cdb71f6e63bc58ad600e420e"><div class="ttname"><a href="QuEST__validation_8c.html#aefc4a3a9cdb71f6e63bc58ad600e420e">validateControlTarget</a></div><div class="ttdeci">void validateControlTarget(Qureg qureg, int controlQubit, int targetQubit, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00408">QuEST_validation.c:408</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a42607270d63948acf84d6def787213e8"><div class="ttname"><a href="QuEST__qasm_8c.html#a42607270d63948acf84d6def787213e8">qasm_recordAxisRotation</a></div><div class="ttdeci">void qasm_recordAxisRotation(Qureg qureg, qreal angle, Vector axis, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00224">QuEST_qasm.c:224</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fab656861dfb036cbcf7009f02a8949253"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fab656861dfb036cbcf7009f02a8949253">GATE_SQRT_SWAP</a></div><div class="ttdeci">@ GATE_SQRT_SWAP</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00034">QuEST_qasm.h:34</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a3ed30f823a59890be17441d97ce90c5c"><div class="ttname"><a href="QuEST__internal_8h.html#a3ed30f823a59890be17441d97ce90c5c">statevec_multiControlledMultiRotateZ</a></div><div class="ttdeci">void statevec_multiControlledMultiRotateZ(Qureg qureg, long long int ctrlMask, long long int targMask, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu_8c_source.html#l03358">QuEST_cpu.c:3358</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fa13c9487aed515148e7594e35eb8dcc55"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa13c9487aed515148e7594e35eb8dcc55">GATE_SIGMA_X</a></div><div class="ttdeci">@ GATE_SIGMA_X</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00021">QuEST_qasm.h:21</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a2d96b4601cc3a9e1221e11a366fe1699"><div class="ttname"><a href="QuEST__common_8c.html#a2d96b4601cc3a9e1221e11a366fe1699">statevec_tGate</a></div><div class="ttdeci">void statevec_tGate(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00275">QuEST_common.c:275</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a0bd6443ea0f5e36738f3b39b72080b6e"><div class="ttname"><a href="QuEST__validation_8c.html#a0bd6443ea0f5e36738f3b39b72080b6e">validateControlState</a></div><div class="ttdeci">void validateControlState(int *controlState, int numControlQubits, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00468">QuEST_validation.c:468</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a6776217a5f7ba38b56175cf6db0f96e0"><div class="ttname"><a href="QuEST__validation_8c.html#a6776217a5f7ba38b56175cf6db0f96e0">validateMultiTargets</a></div><div class="ttdeci">void validateMultiTargets(Qureg qureg, int *targetQubits, int numTargetQubits, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00428">QuEST_validation.c:428</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_ae776148507b8f769cd00d1603212a028"><div class="ttname"><a href="QuEST__qasm_8c.html#ae776148507b8f769cd00d1603212a028">qasm_recordControlledParamGate</a></div><div class="ttdeci">void qasm_recordControlledParamGate(Qureg qureg, TargetGate gate, int controlQubit, int targetQubit, qreal param)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00248">QuEST_qasm.c:248</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_adf5fbea75826cde7d86fd7c31bcf3dec"><div class="ttname"><a href="QuEST__common_8c.html#adf5fbea75826cde7d86fd7c31bcf3dec">statevec_rotateAroundAxis</a></div><div class="ttdeci">void statevec_rotateAroundAxis(Qureg qureg, int rotQubit, qreal angle, Vector axis)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00314">QuEST_common.c:314</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a9fd917537204e074119d4f283dea78e3"><div class="ttname"><a href="QuEST__common_8c.html#a9fd917537204e074119d4f283dea78e3">setConjugateMatrixN</a></div><div class="ttdeci">void setConjugateMatrixN(ComplexMatrixN m)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00115">QuEST_common.c:115</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a3eadcb581f2623e21e4967f791d0439c"><div class="ttname"><a href="QuEST__internal_8h.html#a3eadcb581f2623e21e4967f791d0439c">statevec_multiControlledTwoQubitUnitary</a></div><div class="ttdeci">void statevec_multiControlledTwoQubitUnitary(Qureg qureg, long long int ctrlMask, int targetQubit1, int targetQubit2, ComplexMatrix4 u)</div><div class="ttdoc">This calls swapQubitAmps only when it would involve a distributed communication; if the qubit chunks ...</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01458">QuEST_cpu_distributed.c:1458</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a33be8162c9633bb8015f06b38cf70735"><div class="ttname"><a href="QuEST__qasm_8c.html#a33be8162c9633bb8015f06b38cf70735">qasm_recordControlledAxisRotation</a></div><div class="ttdeci">void qasm_recordControlledAxisRotation(Qureg qureg, qreal angle, Vector axis, int controlQubit, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00301">QuEST_qasm.c:301</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_acc45bb8300922ea5933e294921e25ea2"><div class="ttname"><a href="QuEST__common_8c.html#acc45bb8300922ea5933e294921e25ea2">getQubitBitMask</a></div><div class="ttdeci">long long int getQubitBitMask(int *qubits, int numQubits)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00050">QuEST_common.c:50</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_aec63559e8b9ab0e17efe18d64d2ceca6"><div class="ttname"><a href="QuEST__internal_8h.html#aec63559e8b9ab0e17efe18d64d2ceca6">statevec_compactUnitary</a></div><div class="ttdeci">void statevec_compactUnitary(Qureg qureg, int targetQubit, Complex alpha, Complex beta)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l00858">QuEST_cpu_distributed.c:858</a></div></div>
<div class="ttc" id="agroup__type_html_gga1c703cf89629e4e9c7023cd402d67028a2c64a9aaee27f6bcfef894d159e759bd"><div class="ttname"><a href="group__type.html#gga1c703cf89629e4e9c7023cd402d67028a2c64a9aaee27f6bcfef894d159e759bd">PAULI_Y</a></div><div class="ttdeci">@ PAULI_Y</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00096">QuEST.h:96</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a2153d8611247dd3a2ef483355265cc99"><div class="ttname"><a href="QuEST__common_8c.html#a2153d8611247dd3a2ef483355265cc99">statevec_multiRotatePauli</a></div><div class="ttdeci">void statevec_multiRotatePauli(Qureg qureg, int *targetQubits, enum pauliOpType *targetPaulis, int numTargets, qreal angle, int applyConj)</div><div class="ttdoc">applyConj=1 will apply conjugate operation, else applyConj=0</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00414">QuEST_common.c:414</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_ac4ee5979d475e8c729294b8ef7e0270d"><div class="ttname"><a href="QuEST__internal_8h.html#ac4ee5979d475e8c729294b8ef7e0270d">statevec_multiControlledPhaseFlip</a></div><div class="ttdeci">void statevec_multiControlledPhaseFlip(Qureg qureg, int *controlQubits, int numControlQubits)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu_8c_source.html#l03718">QuEST_cpu.c:3718</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a9a385fde708958617bbeb599064b8dcb"><div class="ttname"><a href="QuEST__qasm_8c.html#a9a385fde708958617bbeb599064b8dcb">qasm_recordComment</a></div><div class="ttdeci">void qasm_recordComment(Qureg qureg, char *comment,...)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00121">QuEST_qasm.c:121</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a7a76950824f17e821415070a4bfdad5b"><div class="ttname"><a href="QuEST__common_8c.html#a7a76950824f17e821415070a4bfdad5b">statevec_multiQubitUnitary</a></div><div class="ttdeci">void statevec_multiQubitUnitary(Qureg qureg, int *targets, int numTargets, ComplexMatrixN u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00573">QuEST_common.c:573</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a336c3286d2434fc892ebe20e9fa22a24"><div class="ttname"><a href="QuEST__common_8c.html#a336c3286d2434fc892ebe20e9fa22a24">statevec_controlledRotateAroundAxis</a></div><div class="ttdeci">void statevec_controlledRotateAroundAxis(Qureg qureg, int controlQubit, int targetQubit, qreal angle, Vector axis)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00330">QuEST_common.c:330</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a142b424d903dfaca7a7ac166076f543a"><div class="ttname"><a href="QuEST__common_8c.html#a142b424d903dfaca7a7ac166076f543a">statevec_sGateConj</a></div><div class="ttdeci">void statevec_sGateConj(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00282">QuEST_common.c:282</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a2cbfe9f416d4d8acb56213841f62cb53"><div class="ttname"><a href="QuEST__common_8c.html#a2cbfe9f416d4d8acb56213841f62cb53">statevec_rotateAroundAxisConj</a></div><div class="ttdeci">void statevec_rotateAroundAxisConj(Qureg qureg, int rotQubit, qreal angle, Vector axis)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00321">QuEST_common.c:321</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a6fa6f1bc617e9fef3cd87ecc3677a02b"><div class="ttname"><a href="QuEST__common_8c.html#a6fa6f1bc617e9fef3cd87ecc3677a02b">getControlFlipMask</a></div><div class="ttdeci">long long int getControlFlipMask(int *controlQubits, int *controlState, int numControlQubits)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00060">QuEST_common.c:60</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a3a79e4305d35f1756b8438bbd34ea6cc"><div class="ttname"><a href="QuEST__qasm_8c.html#a3a79e4305d35f1756b8438bbd34ea6cc">qasm_recordMultiControlledUnitary</a></div><div class="ttdeci">void qasm_recordMultiControlledUnitary(Qureg qureg, ComplexMatrix2 u, int *controlQubits, int numControlQubits, int targetQubit)</div><div class="ttdoc">additionally performs Rz on target to restore the global phase lost from u in QASM U(a,...</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00342">QuEST_qasm.c:342</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a1445a08d034806627cc0b5aa0f4f6d3a"><div class="ttname"><a href="QuEST__qasm_8c.html#a1445a08d034806627cc0b5aa0f4f6d3a">qasm_recordMultiControlledParamGate</a></div><div class="ttdeci">void qasm_recordMultiControlledParamGate(Qureg qureg, TargetGate gate, int *controlQubits, int numControlQubits, int targetQubit, qreal param)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00325">QuEST_qasm.c:325</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_abb2eab4af99adcc59be24f4c91c6f6ad"><div class="ttname"><a href="QuEST__internal_8h.html#abb2eab4af99adcc59be24f4c91c6f6ad">statevec_controlledNot</a></div><div class="ttdeci">void statevec_controlledNot(Qureg qureg, int controlQubit, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01075">QuEST_cpu_distributed.c:1075</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a654db9d60abdcae26427e7d3b3d9c432"><div class="ttname"><a href="QuEST__validation_8c.html#a654db9d60abdcae26427e7d3b3d9c432">validateTwoQubitUnitaryMatrix</a></div><div class="ttdeci">void validateTwoQubitUnitaryMatrix(Qureg qureg, ComplexMatrix4 u, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00481">QuEST_validation.c:481</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_aa32eed5bc38e85193e1aa23b74e8541b"><div class="ttname"><a href="QuEST__common_8c.html#aa32eed5bc38e85193e1aa23b74e8541b">statevec_controlledRotateX</a></div><div class="ttdeci">void statevec_controlledRotateX(Qureg qureg, int controlQubit, int targetQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00346">QuEST_common.c:346</a></div></div>
<div class="ttc" id="astructQureg_html_acf78445e9435d09f44f0cc832c6aee79"><div class="ttname"><a href="structQureg.html#acf78445e9435d09f44f0cc832c6aee79">Qureg::isDensityMatrix</a></div><div class="ttdeci">int isDensityMatrix</div><div class="ttdoc">Whether this instance is a density-state representation.</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00325">QuEST.h:325</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_af3fc7bd149c70f083b149050242cd55e"><div class="ttname"><a href="QuEST__internal_8h.html#af3fc7bd149c70f083b149050242cd55e">statevec_hadamard</a></div><div class="ttdeci">void statevec_hadamard(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01258">QuEST_cpu_distributed.c:1258</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a1f0db2800d13b6c2b120e05129cd13cb"><div class="ttname"><a href="QuEST__common_8c.html#a1f0db2800d13b6c2b120e05129cd13cb">statevec_rotateY</a></div><div class="ttdeci">void statevec_rotateY(Qureg qureg, int rotQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00302">QuEST_common.c:302</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a600bda10463e2078ce746ec28f2d39c9"><div class="ttname"><a href="QuEST__internal_8h.html#a600bda10463e2078ce746ec28f2d39c9">statevec_multiControlledUnitary</a></div><div class="ttdeci">void statevec_multiControlledUnitary(Qureg qureg, long long int ctrlQubitsMask, long long int ctrlFlipMask, int targetQubit, ComplexMatrix2 u)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01011">QuEST_cpu_distributed.c:1011</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a0344fbbb2bb505f7db14b420153f1eb5"><div class="ttname"><a href="QuEST__validation_8c.html#a0344fbbb2bb505f7db14b420153f1eb5">validateOneQubitUnitaryMatrix</a></div><div class="ttdeci">void validateOneQubitUnitaryMatrix(ComplexMatrix2 u, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00477">QuEST_validation.c:477</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a33cde9b6518d55a544eff20301a5d844"><div class="ttname"><a href="QuEST__common_8c.html#a33cde9b6518d55a544eff20301a5d844">statevec_sqrtSwapGateConj</a></div><div class="ttdeci">void statevec_sqrtSwapGateConj(Qureg qureg, int qb1, int qb2)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00400">QuEST_common.c:400</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a3e11a9b9fa5ee16d4738a97f4590ee61"><div class="ttname"><a href="QuEST__common_8c.html#a3e11a9b9fa5ee16d4738a97f4590ee61">statevec_controlledRotateZ</a></div><div class="ttdeci">void statevec_controlledRotateZ(Qureg qureg, int controlQubit, int targetQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00358">QuEST_common.c:358</a></div></div>
<div class="ttc" id="astructQureg_html_ad08dff5316b8937f4b2a1417591543dc"><div class="ttname"><a href="structQureg.html#ad08dff5316b8937f4b2a1417591543dc">Qureg::numQubitsRepresented</a></div><div class="ttdeci">int numQubitsRepresented</div><div class="ttdoc">The number of qubits represented in either the state-vector or density matrix.</div><div class="ttdef"><b>Definition:</b> <a href="QuEST_8h_source.html#l00327">QuEST.h:327</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a1c82b5e914a8a39c5c7b782dbc16fa76"><div class="ttname"><a href="QuEST__internal_8h.html#a1c82b5e914a8a39c5c7b782dbc16fa76">statevec_pauliX</a></div><div class="ttdeci">void statevec_pauliX(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01048">QuEST_cpu_distributed.c:1048</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a5b0392701c555a898403f80ef4a32f62"><div class="ttname"><a href="QuEST__validation_8c.html#a5b0392701c555a898403f80ef4a32f62">validateMultiControlsMultiTargets</a></div><div class="ttdeci">void validateMultiControlsMultiTargets(Qureg qureg, int *controlQubits, int numControlQubits, int *targetQubits, int numTargetQubits, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00459">QuEST_validation.c:459</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fa5053f3d968443bc04e8b1d09f18bab9a"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fa5053f3d968443bc04e8b1d09f18bab9a">GATE_S</a></div><div class="ttdeci">@ GATE_S</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00025">QuEST_qasm.h:25</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fab12d052de2b7c59c6ab87710fd7d3c78"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fab12d052de2b7c59c6ab87710fd7d3c78">GATE_SWAP</a></div><div class="ttdeci">@ GATE_SWAP</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00033">QuEST_qasm.h:33</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_aaf78491e35d165edfd57387f9fffecbd"><div class="ttname"><a href="QuEST__internal_8h.html#aaf78491e35d165edfd57387f9fffecbd">statevec_controlledPhaseFlip</a></div><div class="ttdeci">void statevec_controlledPhaseFlip(Qureg qureg, int idQubit1, int idQubit2)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu_8c_source.html#l03687">QuEST_cpu.c:3687</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725faa29b98cbb581abf5ec338a1763de7a1b"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725faa29b98cbb581abf5ec338a1763de7a1b">GATE_SIGMA_Y</a></div><div class="ttdeci">@ GATE_SIGMA_Y</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00022">QuEST_qasm.h:22</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a518c4351d574aea8477019dbce02f09c"><div class="ttname"><a href="QuEST__qasm_8c.html#a518c4351d574aea8477019dbce02f09c">qasm_recordCompactUnitary</a></div><div class="ttdeci">void qasm_recordCompactUnitary(Qureg qureg, Complex alpha, Complex beta, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00196">QuEST_qasm.c:196</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a5e99d405002cdf6ddd40922911d058a4"><div class="ttname"><a href="QuEST__qasm_8c.html#a5e99d405002cdf6ddd40922911d058a4">qasm_recordControlledUnitary</a></div><div class="ttdeci">void qasm_recordControlledUnitary(Qureg qureg, ComplexMatrix2 u, int controlQubit, int targetQubit)</div><div class="ttdoc">additionally performs Rz on target to restore the global phase lost from u in QASM U(a,...</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00279">QuEST_qasm.c:279</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_ade67874c89179541f616b3685595d3ae"><div class="ttname"><a href="QuEST__common_8c.html#ade67874c89179541f616b3685595d3ae">statevec_controlledRotateY</a></div><div class="ttdeci">void statevec_controlledRotateY(Qureg qureg, int controlQubit, int targetQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00352">QuEST_common.c:352</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a5ea2384a9b33c94eac891aacbfa5da6a"><div class="ttname"><a href="QuEST__common_8c.html#a5ea2384a9b33c94eac891aacbfa5da6a">statevec_controlledRotateAroundAxisConj</a></div><div class="ttdeci">void statevec_controlledRotateAroundAxisConj(Qureg qureg, int controlQubit, int targetQubit, qreal angle, Vector axis)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00337">QuEST_common.c:337</a></div></div>
<div class="ttc" id="aQuEST__qasm_8c_html_a81749d23b8c3c1acf87c9db675872c24"><div class="ttname"><a href="QuEST__qasm_8c.html#a81749d23b8c3c1acf87c9db675872c24">qasm_recordGate</a></div><div class="ttdeci">void qasm_recordGate(Qureg qureg, TargetGate gate, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8c_source.html#l00179">QuEST_qasm.c:179</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_aa194ba5f5c6e19c6caa4c715b3dbefcc"><div class="ttname"><a href="QuEST__validation_8c.html#aa194ba5f5c6e19c6caa4c715b3dbefcc">validatePauliCodes</a></div><div class="ttdeci">void validatePauliCodes(enum pauliOpType *pauliCodes, int numPauliCodes, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00599">QuEST_validation.c:599</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_a5d49d4aadea858794b139c6a195ffd8b"><div class="ttname"><a href="QuEST__validation_8c.html#a5d49d4aadea858794b139c6a195ffd8b">validateUnitaryComplexPair</a></div><div class="ttdeci">void validateUnitaryComplexPair(Complex alpha, Complex beta, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00507">QuEST_validation.c:507</a></div></div>
<div class="ttc" id="aQuEST__qasm_8h_html_a32bbd0276b80668812ac248cd81c725fae1267d5de573dc2901aa8e724ac1d689"><div class="ttname"><a href="QuEST__qasm_8h.html#a32bbd0276b80668812ac248cd81c725fae1267d5de573dc2901aa8e724ac1d689">GATE_ROTATE_Y</a></div><div class="ttdeci">@ GATE_ROTATE_Y</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__qasm_8h_source.html#l00028">QuEST_qasm.h:28</a></div></div>
<div class="ttc" id="aQuEST__common_8c_html_a2b2b8c69566a49cdf4a3fa2cb4f5e03c"><div class="ttname"><a href="QuEST__common_8c.html#a2b2b8c69566a49cdf4a3fa2cb4f5e03c">statevec_rotateZ</a></div><div class="ttdeci">void statevec_rotateZ(Qureg qureg, int rotQubit, qreal angle)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__common_8c_source.html#l00308">QuEST_common.c:308</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a1275d604674224d87a173fb5bac78835"><div class="ttname"><a href="QuEST__internal_8h.html#a1275d604674224d87a173fb5bac78835">statevec_controlledCompactUnitary</a></div><div class="ttdeci">void statevec_controlledCompactUnitary(Qureg qureg, int controlQubit, int targetQubit, Complex alpha, Complex beta)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l00934">QuEST_cpu_distributed.c:934</a></div></div>
<div class="ttc" id="aQuEST__validation_8c_html_aed5f85789dc4fa43b64e99e6b538035c"><div class="ttname"><a href="QuEST__validation_8c.html#aed5f85789dc4fa43b64e99e6b538035c">validateUniqueTargets</a></div><div class="ttdeci">void validateUniqueTargets(Qureg qureg, int qubit1, int qubit2, const char *caller)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__validation_8c_source.html#l00414">QuEST_validation.c:414</a></div></div>
<div class="ttc" id="aQuEST__internal_8h_html_a81fbd2eccd0d0e5a3cece4df2f96cb92"><div class="ttname"><a href="QuEST__internal_8h.html#a81fbd2eccd0d0e5a3cece4df2f96cb92">statevec_pauliYConj</a></div><div class="ttdeci">void statevec_pauliYConj(Qureg qureg, int targetQubit)</div><div class="ttdef"><b>Definition:</b> <a href="QuEST__cpu__distributed_8c_source.html#l01167">QuEST_cpu_distributed.c:1167</a></div></div>
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