CompMatr1

Functions for applying general one-qubit dense matrices, as CompMatr1. More...

Functions
void	applyCompMatr1 (Qureg qureg, int target, CompMatr1 matrix)
void	applyControlledCompMatr1 (Qureg qureg, int control, int target, CompMatr1 matrix)
void	applyMultiControlledCompMatr1 (Qureg qureg, int *controls, int numControls, int target, CompMatr1 matrix)
void	applyMultiStateControlledCompMatr1 (Qureg qureg, int *controls, int *states, int numControls, int target, CompMatr1 matrix)
void	multiplyCompMatr1 (Qureg qureg, int target, CompMatr1 matrix)

Detailed Description

Functions for applying general one-qubit dense matrices, as CompMatr1.

Function Documentation

applyCompMatr1()

void applyCompMatr1	(	Qureg	qureg,
		int	target,
		CompMatr1	matrix )

Applies a general one-qubit dense unitary matrix to the specified target qubit of qureg.

Diagram

Formulae

Let \( \hat{U} = \) matrix, \( t = \) target, and let \(\hat{U}_t\) notate operating \(\hat{U}\) upon the \( t \)-th qubit among \( N \), i.e.

\[ \hat{U}_t \equiv \id^{N-t} \otimes \hat{U} \otimes \id^{t-1}. \]

Then,

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

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

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

  \[ \dmrho \rightarrow \hat{U}_t \, \dmrho \, {\hat{U}_t}^\dagger. \]

Constraints

• Unitarity of \( \hat{U} = \) matrix requires that \( \hat{U} \hat{U}^\dagger = \id \). Validation will check that matrix is approximately unitarity via

  \[ \max\limits_{ij} \Big|\left(\hat{U} \hat{U}^\dagger - \id\right)_{ij}\Big|^2 \le \valeps \]

  where the validation epsilon \( \valeps \) can be adjusted with setValidationEpsilon().

Example

Qureg qureg = createQureg(5);
 
CompMatr1 matrix = getInlineCompMatr1({
    {-1i/sqrt(2), 1i/sqrt(2)},
    {(1i-1)/2,    (1i-1)/2}
});
 
applyCompMatr1(qureg, 2, matrix); 

Parameters

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

Exceptions

invalidQuESTInputError()

if qureg or matrix are uninitialised. if matrix is not approximately unitary. if target is an invalid qubit index.

See also

• getCompMatr1()
• getInlineCompMatr1()
• multiplyCompMatr1()
• applyControlledCompMatr1()
• applyCompMatr2()
• applyCompMatr()

Author

Tyson Jones

Definition at line 86 of file operations.cpp.

                                                               {
 
    validateAndApplyAnyCtrlAnyTargUnitaryMatrix(qureg, nullptr, nullptr, 0, &target, 1, matrix, __func__);
}

Referenced by TEST_CASE().

applyControlledCompMatr1()

void applyControlledCompMatr1	(	Qureg	qureg,
		int	control,
		int	target,
		CompMatr1	matrix )

Applies a singly-controlled one-qubit dense unitary matrix to the specified target qubit of qureg.

Diagram

Note

Documentation for this function or struct is under construction!

Definition at line 91 of file operations.cpp.

                                                                                      {
 
    validateAndApplyAnyCtrlAnyTargUnitaryMatrix(qureg, &control, nullptr, 1, &target, 1, matrix, __func__);
}

applyMultiControlledCompMatr1()

void applyMultiControlledCompMatr1	(	Qureg	qureg,
		int *	controls,
		int	numControls,
		int	target,
		CompMatr1	matrix )

Applies a multiply-controlled one-qubit dense unitary matrix to the specified target qubit of qureg.

Diagram

Note

Documentation for this function or struct is under construction!

Definition at line 96 of file operations.cpp.

                                                                                                              {
 
    validateAndApplyAnyCtrlAnyTargUnitaryMatrix(qureg, controls, nullptr, numControls, &target, 1, matrix, __func__);
}

applyMultiStateControlledCompMatr1()

void applyMultiStateControlledCompMatr1	(	Qureg	qureg,
		int *	controls,
		int *	states,
		int	numControls,
		int	target,
		CompMatr1	matrix )

Applies an arbitrarily-controlled one-qubit dense unitary matrix to the specified target qubit of qureg, conditioned upon the controls being in the given states.

Diagram

Note

Documentation for this function or struct is under construction!

Definition at line 101 of file operations.cpp.

                                                                                                                                {
 
    validateAndApplyAnyCtrlAnyTargUnitaryMatrix(qureg, controls, states, numControls, &target, 1, matrix, __func__);
}

Referenced by applyMultiStateControlledRotateAroundAxis().

multiplyCompMatr1()

void multiplyCompMatr1	(	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}
});
 
multiplyCompMatr1(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.

Exceptions

invalidQuESTInputError()

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

See also

• getCompMatr1()
• getInlineCompMatr1()
• applyCompMatr1()
• applyQubitProjector()
• multiplyCompMatr()

Author

Tyson Jones

Definition at line 77 of file operations.cpp.

                                                                  {
    validate_quregFields(qureg, __func__);
    validate_target(qureg, target, __func__);
    validate_matrixFields(matrix, __func__); // matrix can be non-unitary
 
    bool conj = false;
    localiser_statevec_anyCtrlOneTargDenseMatr(qureg, {}, {}, target, matrix, conj);
}