CompMatr1

Functions for pre- or post-multiplying general one-qubit dense matrices (as CompMatr1) upon density matrices. More...

Functions
void	leftapplyCompMatr1 (Qureg qureg, int target, CompMatr1 matrix)
void	rightapplyCompMatr1 (Qureg qureg, int target, CompMatr1 matrix)

Detailed Description

Functions for pre- or post-multiplying general one-qubit dense matrices (as CompMatr1) upon density matrices.

Function Documentation

leftapplyCompMatr1()

void leftapplyCompMatr1	(	Qureg	qureg,
		int	target,
		CompMatr1	matrix )

Multiplies a general one-qubit dense matrix upon the specified target qubit of qureg.

Formulae

Let \( \hat{M} = \) matrix and \( t = \) target, and notate \(\hat{M}_t\) as per applyCompMatr1(). Unlike applyCompMatr1() however, this function only ever left-multiplies matrix upon qureg, regardless of whether it is a statevector or density matrix.

Explicitly,

• When qureg is a statevector \( \svpsi \), this function effects

  \[ \svpsi \rightarrow \hat{M}_t \, \svpsi. \]

• When qureg is a density matrix \(\dmrho\), this function effects

  \[ \dmrho \rightarrow \hat{M}_t \, \dmrho. \]

There are no additional constraints like unitarity.

Example

Qureg qureg = createDensityQureg(5);
 
CompMatr1 matrix = getInlineCompMatr1({
    {0.1, 0.2},
    {0.3i, 0.4i}
});
 
leftapplyCompMatr1(qureg, 2, matrix); 

Parameters

[in,out]	qureg	the state to modify.
[in]	target	the index of the target qubit.
[in]	matrix	the Z-basis matrix to multiply upon the left.

Exceptions

error

if qureg or matrix are uninitialised. if target is an invalid qubit index.

See also

• getCompMatr1()
• getInlineCompMatr1()
• applyCompMatr1()
• rightapplyCompMatr1()
• applyQubitProjector()
• leftapplyCompMatr()

Author

Tyson Jones

Definition at line 31 of file multiplication.cpp.

                                                                   {
    validate_quregFields(qureg, __func__);
    validate_target(qureg, target, __func__);
    validate_matrixFields(matrix, __func__);
 
    bool conj = false;
    bool transp = false;
    localiser_statevec_anyCtrlOneTargDenseMatr(qureg, {}, {}, target, matrix, conj, transp);
}

rightapplyCompMatr1()

void rightapplyCompMatr1	(	Qureg	qureg,
		int	target,
		CompMatr1	matrix )

Multiplies a general one-qubit dense matrix upon the specified target qubit of the density matrix qureg, from the right-hand side.

Formulae

Let \( \dmrho = \) qureg, \( \hat{M} = \) matrix and \( t = \) target, and notate \(\hat{M}_t\) as per applyCompMatr1(). Unlike applyCompMatr1() however, this function only ever right-multiplies matrix upon qureg.

Explicitly

\[ \dmrho \rightarrow \dmrho \, \hat{M}_t \]

where \( \hat{M} \) is not conjugated nor transposed, and there are no additional constraints like unitarity.

In general, this function will break the normalisation of qureg and result in a non-physical state, and is useful for preparing sub-expressions of formulae like the Linbladian.

Example

Qureg qureg = createDensityQureg(5);
 
CompMatr1 matrix = getInlineCompMatr1({
    {0.1, 0.2},
    {0.3i, 0.4i}
});
 
rightapplyCompMatr1(qureg, 2, matrix); 

Parameters

[in,out]	qureg	the state to modify.
[in]	target	the index of the target qubit.
[in]	matrix	the Z-basis matrix to post-multiply.

Exceptions

error

if qureg or matrix are uninitialised. if qureg is not a density matrix. if target is an invalid qubit index.

See also

• getCompMatr1()
• getInlineCompMatr1()
• applyCompMatr1()
• leftapplyCompMatr1()
• leftapplyCompMatr()

Author

Tyson Jones

Definition at line 41 of file multiplication.cpp.

                                                                    {
    validate_quregFields(qureg, __func__);
    validate_quregIsDensityMatrix(qureg, __func__);
    validate_target(qureg, target, __func__);
    validate_matrixFields(matrix, __func__);
    
    // rho matrix ~ transpose(rho) (x) I ||rho>>
    bool conj = false;
    bool transp = true;
    int qubit = util_getBraQubit(target, qureg);
    localiser_statevec_anyCtrlOneTargDenseMatr(qureg, {}, {}, qubit, matrix, conj, transp);
}