Function multiControlledMultiRotatePauli

pub unsafe extern "C" fn multiControlledMultiRotatePauli(
    qureg: Qureg,
    controlQubits: *mut c_int,
    numControls: c_int,
    targetQubits: *mut c_int,
    targetPaulis: *mut pauliOpType,
    numTargets: c_int,
    angle: f64,
)

Apply a multi-controlled multi-target multi-Pauli rotation, also known as a controlled Pauli gadget. This is the unitary \f[ |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} \f] where \f$\hat{\sigma}_j\f$ are the Pauli operators (::pauliOpType) in targetPaulis, which operate upon the corresponding qubits in targetQubits.

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All qubits not appearing in \p targetQubits and \p controlQubits are assumed to receive the identity operator.

For example:

    int numCtrls = 1;
    int numTargs = 4;
    int ctrls[] = {4};
    int targs[] = {0,1,2,3};

    pauliOpType paulis[] = {PAULI_X, PAULI_Y, PAULI_Z, PAULI_I};

    multiControlledMultiRotatePauli(
        qureg, ctrls, numCtrls, targs, paulis, numTargs, 0.1);

effects \f[ |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} \f] on \p qureg, where unspecified qubits (along with those targeted by PAULI_I) are assumed to receive the identity operator (excluded from exponentiation).

This means specifying PAULI_I does not induce a global phase factor \f$\exp(-i \theta/2)\f$. Hence, if all \p targetPaulis are identity, then this function does nothing to \p qureg. Specifying PAULI_I on a qubit is superfluous but allowed for convenience.

This function effects the controlled Pauli gadget by first (controlled) rotating the qubits which are targeted with either X or Y into alternate basis, performing multiControlledMultiRotateZ() on all target qubits, then restoring the original basis.

@see

• multiControlledMultiRotateZ()
• multiRotatePauli()
• multiRotateZ()
• rotateX()
• rotateY()
• rotateZ()
• rotateAroundAxis()

@ingroup unitary @param[in,out] qureg object representing the set of all qubits @param[in] controlQubits list of the indices of qubits to control upon @param[in] numControls length of length controlQubits @param[in] targetQubits a list of the indices of the target qubits @param[in] targetPaulis a list of the Pauli operators around which to rotate the target qubits @param[in] numTargets length of list targetQubits @param[in] angle the angle by which the multi-qubit state is rotated around the Z axis @throws invalidQuESTInputError()

• if any qubit in \p controlQubits and \p targetQubits is invalid, i.e. outside [0, qureg.numQubitsRepresented)
• if \p controlQubits or \p targetQubits contain any repetitions
• if any qubit in \p controlQubits is also in \p targetQubits (and vice versa)
• if \p numTargets < 1
• if \p numControls < 1 (use multiRotateZ() for no controls)
• if any element of \p targetPaulis is not one of PAULI_I, PAULI_X, PAULI_Y, PAULI_Z @throws segmentation-fault
• if \p controlQubits contains fewer elements than \p numControls
• if \p targetQubits contains fewer elements than \p numTargets
• if \p targetPaulis contains fewer elements than \p numTargets @author Tyson Jones