Function applyPauliSum

pub unsafe extern "C" fn applyPauliSum(
    inQureg: Qureg,
    allPauliCodes: *mut pauliOpType,
    termCoeffs: *mut f64,
    numSumTerms: c_int,
    outQureg: Qureg,
)

Modifies \p outQureg to be the result of applying the weighted sum of Pauli products (a Hermitian but not necessarily unitary operator) to \p inQureg. Note that afterward, \p outQureg may no longer be normalised and ergo not a state-vector or density matrix. Users must therefore be careful passing \p outQureg to other QuEST functions which assume normalisation in order to function correctly.

Letting \f$ \alpha = \sum_i c_i \otimes_j^{N} \hat{\sigma}_{i,j} \f$ be the operators indicated by \p allPauliCodes (where \f$ c_i \in \f$ \p termCoeffs and \f$ N = \f$ \p qureg.numQubitsRepresented), this function effects \f$ \alpha | \psi \rangle \f$ on state-vector \f$ |\psi\rangle \f$ and \f$\alpha \rho\f$ (left matrix multiplication) on density matrix \f$ \rho \f$.

\p allPauliCodes is an array of length \p numSumTerms*\p qureg.numQubitsRepresented which specifies which Pauli operators to apply, where 0 = \p PAULI_I, 1 = \p PAULI_X, 2 = \p PAULI_Y, 3 = \p PAULI_Z. For each sum term, a Pauli operator must be specified for EVERY qubit in \p qureg; each set of \p numSumTerms operators will be grouped into a product. \p termCoeffs is an arrray of length \p numSumTerms containing the term coefficients. For example, on a 3-qubit state-vector,

    int paulis[6] = {PAULI_X, PAULI_I, PAULI_I,  PAULI_X, PAULI_Y, PAULI_Z};
    qreal coeffs[2] = {1.5, -3.6};
    applyPauliSum(inQureg, paulis, coeffs, 2, outQureg);

will apply Hermitian operation \f$ (1.5 X I I - 3.6 X Y Z) \f$ (where in this notation, the left-most operator applies to the least-significant qubit, i.e. that with index 0).

In theory, \p inQureg is unchanged though its state is temporarily modified and is reverted by re-applying Paulis (XX=YY=ZZ=I), so may see a change by small numerical errors. The initial state in \p outQureg is not used.

\p inQureg and \p outQureg must both be state-vectors, or both density matrices, of equal dimensions. \p inQureg cannot be \p outQureg.

This function works by applying each Pauli product to \p inQureg in turn, and adding the resulting state (weighted by a coefficient in \p termCoeffs) to the initially-blanked \p outQureg. Ergo it should scale with the total number of Pauli operators specified (excluding identities), and the qureg dimension.

@see

• calcExpecPauliSum()
• applyPauliHamil()

@ingroup operator @param[in] inQureg the register containing the state which \p outQureg will be set to, under the action of the Hermitiain operator specified by the Pauli codes. \p inQureg should be unchanged, though may vary slightly due to numerical error. @param[in] allPauliCodes a list of the Pauli codes (0=PAULI_I, 1=PAULI_X, 2=PAULI_Y, 3=PAULI_Z) of all Paulis involved in the products of terms. A Pauli must be specified for each qubit in the register, in every term of the sum. @param[in] termCoeffs The coefficients of each term in the sum of Pauli products @param[in] numSumTerms The total number of Pauli products specified @param[out] outQureg the qureg to modify to be the result of applyling the weighted Pauli sum operator to the state in \p inQureg @throws invalidQuESTInputError()

• if any code in \p allPauliCodes is not in {0,1,2,3}
• if numSumTerms <= 0
• if \p inQureg is not of the same type and dimensions as \p outQureg @author Tyson Jones