Operators

Non-physical operators which may be non-unitary, non-norm-preserving, even non-Hermitian. More...

Functions
void	applyPauliSum (Qureg inQureg, enum pauliOpType *allPauliCodes, qreal *termCoeffs, int numSumTerms, Qureg outQureg)
	Modifies outQureg to be the result of applying the weighted sum of Pauli products (a Hermitian but not necessarily unitary operator) to inQureg. More...

Detailed Description

Non-physical operators which may be non-unitary, non-norm-preserving, even non-Hermitian.

Function Documentation

applyPauliSum()

void applyPauliSum	(	Qureg	inQureg,
		enum pauliOpType *	allPauliCodes,
		qreal *	termCoeffs,
		int	numSumTerms,
		Qureg	outQureg
	)

Modifies outQureg to be the result of applying the weighted sum of Pauli products (a Hermitian but not necessarily unitary operator) to inQureg.

Note that afterward, outQureg may no longer be normalised and ergo not a statevector or density matrix. Users must therefore be careful passing outQureg to other QuEST functions which assume normalisation in order to function correctly.

Letting be the operators indicated by allPauliCodes (where termCoeffs and qureg.numQubitsRepresented), this function effects on statevector and (left matrix multiplication) on density matrix .

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

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 (where in this notation, the left-most operator applies to the least-significant qubit, i.e. that with index 0).

In theory, 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 outQureg is not used.

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

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

Parameters

[in]	inQureg	the register containing the state which outQureg will be set to, under the action of the Hermitiain operator specified by the Pauli codes. inQureg should be unchanged, though may vary slightly due to numerical error.
[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.
[in]	termCoeffs	The coefficients of each term in the sum of Pauli products
[in]	numSumTerms	The total number of Pauli products specified
[out]	outQureg	the qureg to modify to be the result of applyling the weighted Pauli sum operator to the state in inQureg

Exceptions

exitWithError

if any code in allPauliCodes is not in {0,1,2,3}, or if numSumTerms <= 0, or if inQureg is not of the same type and dimensions as outQureg

Author

Tyson Jones

Definition at line 806 of file QuEST.c.

                                                                                                                       {
    validateMatchingQuregTypes(inQureg, outQureg, __func__);
    validateMatchingQuregDims(inQureg, outQureg, __func__);
    validateNumPauliSumTerms(numSumTerms, __func__);
    validatePauliCodes(allPauliCodes, numSumTerms*inQureg.numQubitsRepresented, __func__);
    
    statevec_applyPauliSum(inQureg, allPauliCodes, termCoeffs, numSumTerms, outQureg);
    
    qasm_recordComment(outQureg, "Here, the register was modified to an undisclosed and possibly unphysical state (applyPauliSum).");
}

References Qureg::numQubitsRepresented, qasm_recordComment(), statevec_applyPauliSum(), validateMatchingQuregDims(), validateMatchingQuregTypes(), validateNumPauliSumTerms(), and validatePauliCodes().

Referenced by TEST_CASE().