Standard gates

standard_gates

Functions:

Name	Description
H	[Qmod core-library function]
X	[Qmod core-library function]
Y	[Qmod core-library function]
Z	[Qmod core-library function]
I	[Qmod core-library function]
S	[Qmod core-library function]
T	[Qmod core-library function]
SDG	[Qmod core-library function]
TDG	[Qmod core-library function]
PHASE	[Qmod core-library function]
RX	[Qmod core-library function]
RY	[Qmod core-library function]
RZ	[Qmod core-library function]
R	[Qmod core-library function]
RXX	[Qmod core-library function]
RYY	[Qmod core-library function]
RZZ	[Qmod core-library function]
CH	[Qmod core-library function]
CX	[Qmod core-library function]
CY	[Qmod core-library function]
CZ	[Qmod core-library function]
CRX	[Qmod core-library function]
CRY	[Qmod core-library function]
CRZ	[Qmod core-library function]
CPHASE	[Qmod core-library function]
SWAP	[Qmod core-library function]
IDENTITY	[Qmod core-library function]
U	[Qmod core-library function]
CCX	[Qmod core-library function]

H

H(target: QBit) -> None

[Qmod core-library function]

Performs the Hadamard gate on a qubit.

This operation is represented by the following matrix:

\[ H = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the Hadamard gate to.	required

X

X(target: QBit) -> None

[Qmod core-library function]

Performs the Pauli-X gate on a qubit.

This operation is represented by the following matrix:

\[ X = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the Pauli-X gate to.	required

Y

Y(target: QBit) -> None

[Qmod core-library function]

Performs the Pauli-Y gate on a qubit.

This operation is represented by the following matrix:

\[ Y = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the Pauli-Y gate to.	required

Z

Z(target: QBit) -> None

[Qmod core-library function]

Performs the Pauli-Z gate on a qubit.

This operation is represented by the following matrix:

\[ Z = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the Pauli-Z gate to.	required

I

I(target: QBit) -> None

[Qmod core-library function]

Performs the identity gate on a qubit.

This operation is represented by the following matrix:

\[ I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the identity gate to.	required

S

S(target: QBit) -> None

[Qmod core-library function]

Performs the S gate on a qubit.

This operation is represented by the following matrix:

\[ S = \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the S gate to.	required

T

T(target: QBit) -> None

[Qmod core-library function]

Performs the T gate on a qubit.

This operation is represented by the following matrix:

\[ T = \begin{bmatrix} 1 & 0 \\ 0 & e^{i\frac{\pi}{4}} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the T gate to.	required

SDG

SDG(target: QBit) -> None

[Qmod core-library function]

Performs the S-dagger gate on a qubit.

This operation is represented by the following matrix:

\[ S^\dagger = \begin{bmatrix} 1 & 0 \\ 0 & -i \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the S-dagger gate to.	required

TDG

TDG(target: QBit) -> None

[Qmod core-library function]

Performs the T-dagger gate on a qubit.

This operation is represented by the following matrix:

\[ T^\dagger = \begin{bmatrix} 1 & 0 \\ 0 & e^{-i\frac{\pi}{4}} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
target	QBit	The qubit to apply the T-dagger gate to.	required

PHASE

PHASE(theta: CReal, target: QBit) -> None

[Qmod core-library function]

Performs the phase gate on a qubit.

This operation is represented by the following matrix:

\[ PHASE(\theta) = \begin{bmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The phase angle in radians.	required
target	QBit	The qubit to apply the phase gate to.	required

RX

RX(theta: CReal, target: QBit) -> None

[Qmod core-library function]

Performs the Pauli-X rotation gate on a qubit.

This operation is represented by the following matrix:

\[ R_X(\theta) = e^{-i\frac{\theta}{2}X} = \begin{bmatrix} cos(\frac{\theta}{2}) & -i sin(\frac{\theta}{2}) \\ -i sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
target	QBit	The qubit to apply the Pauli-X rotation gate to.	required

RY

RY(theta: CReal, target: QBit) -> None

[Qmod core-library function]

Performs the Pauli-Y rotation gate on a qubit.

This operation is represented by the following matrix:

\[ R_Y(\theta) = e^{-i\frac{\theta}{2}Y} = \begin{bmatrix} cos(\frac{\theta}{2}) & -sin(\frac{\theta}{2}) \\ -sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
target	QBit	The qubit to apply the Pauli-Y rotation gate to.	required

RZ

RZ(theta: CReal, target: QBit) -> None

[Qmod core-library function]

Performs the Pauli-Z rotation gate on a qubit.

This operation is represented by the following matrix:

\[ R_Z(\theta) = e^{-i\frac{\theta}{2}Z} = \begin{bmatrix} e^{-i\frac{\theta}{2}} & 0 \\ 0 & e^{i\frac{\theta}{2}} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
target	QBit	The qubit to apply the Pauli-Z rotation gate to.	required

R

R(theta: CReal, phi: CReal, target: QBit) -> None

[Qmod core-library function]

Performs a rotation of \(\theta\) around the \(cos(\phi)\hat{x} + sin(\phi)\hat{y}\) axis on a qubit.

This operation is represented by the following matrix:

\[ R(\theta, \phi) = e^{-i \frac{\theta}{2} (cos(\phi)X + sin(\phi)Y)} = \begin{bmatrix} cos(\frac{\theta}{2}) & -i e^{-i\phi} sin(\frac{\theta}{2}) \\ -i e^{i\phi} sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
phi	CReal	The phase angle in radians.	required
target	QBit	The qubit to apply the general single-qubit rotation gate to.	required

RXX

RXX(theta: CReal, target: QArray[QBit, Literal[2]]) -> None

[Qmod core-library function]

Performs the XX rotation gate on a pair of qubits.

This operation is represented by the following matrix:

\[ R_{XX}(\theta) = e^{-i\frac{\theta}{2}X \otimes X} = \begin{bmatrix} cos(\frac{\theta}{2}) & 0 & 0 & -i sin(\frac{\theta}{2}) \\ 0 & cos(\frac{\theta}{2}) & -i sin(\frac{\theta}{2}) & 0 \\ 0 & -i sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) & 0 \\ -i sin(\frac{\theta}{2}) & 0 & 0 & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
target	QArray[QBit, Literal[2]]	The pair of qubits to apply the XX rotation gate to.	required

RYY

RYY(theta: CReal, target: QArray[QBit, Literal[2]]) -> None

[Qmod core-library function]

Performs the YY rotation gate on a pair of qubits.

This operation is represented by the following matrix:

\[ R_{YY}(\theta) = e^{-i\frac{\theta}{2}Y \otimes Y} = \begin{bmatrix} cos(\frac{\theta}{2}) & 0 & 0 & -sin(\frac{\theta}{2}) \\ 0 & cos(\frac{\theta}{2}) & sin(\frac{\theta}{2}) & 0 \\ 0 & sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) & 0 \\ -sin(\frac{\theta}{2}) & 0 & 0 & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
target	QArray[QBit, Literal[2]]	The pair of qubits to apply the YY rotation gate to.	required

RZZ

RZZ(theta: CReal, target: QArray[QBit, Literal[2]]) -> None

[Qmod core-library function]

Performs the ZZ rotation gate on a pair of qubits.

This operation is represented by the following matrix:

\[ R_{ZZ}(\theta) = e^{-i\frac{\theta}{2}Z \otimes Z} = \begin{bmatrix} e^{-i\frac{\theta}{2}} & 0 & 0 & 0 \\ 0 & e^{i\frac{\theta}{2}} & 0 & 0 \\ 0 & 0 & e^{i\frac{\theta}{2}} & 0 \\ 0 & 0 & 0 & e^{-i\frac{\theta}{2}} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
target	QArray[QBit, Literal[2]]	The pair of qubits to apply the ZZ rotation gate to.	required

CH

CH(ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the Hadamard gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CH = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & -1 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the Hadamard gate on.	required

CX

CX(ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the Pauli-X gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CX = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the Pauli-X gate on.	required

CY

CY(ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the Pauli-Y gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CY = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & -i \\ 0 & 0 & i & 0 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the Pauli-Y gate on.	required

CZ

CZ(ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the Pauli-Z gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CZ = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the Pauli-Z gate on.	required

CRX

CRX(theta: CReal, ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the RX gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CRX = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & cos(\frac{\theta}{2}) & -i*sin(\frac{\theta}{2}) \\ 0 & 0 & -i*sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the RX gate on.	required

CRY

CRY(theta: CReal, ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the RY gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CRY = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & cos(\frac{\theta}{2}) & -sin(\frac{\theta}{2}) \\ 0 & 0 & sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the RY gate on.	required

CRZ

CRZ(theta: CReal, ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the RZ gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CRZ = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\frac{\theta}{2}} & 0 \\ 0 & 0 & 0 & e^{i\frac{\theta}{2}} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the RZ gate on.	required

CPHASE

CPHASE(theta: CReal, ctrl: QBit, target: QBit) -> None

[Qmod core-library function]

Applies the PHASE gate to the target qubit, conditioned on the control qubit.

This operation is represented by the following matrix:

\[ CPHASE = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\theta} \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The rotation angle in radians.	required
ctrl	QBit	The control qubit.	required
target	QBit	The qubit to apply the PHASE gate on.	required

SWAP

SWAP(qbit0: QBit, qbit1: QBit) -> None

[Qmod core-library function]

Swaps the states of two qubits.

This operation is represented by the following matrix:

\[ SWAP = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
qbit0	QBit	The first qubit.	required
qbit1	QBit	The second qubit.	required

IDENTITY

IDENTITY(target: QArray[QBit]) -> None

[Qmod core-library function]

Does nothing.

This operation is represented by the following matrix:

\[ IDENTITY = {\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}} ^{\otimes n} \]

Parameters:

Name	Type	Description	Default
target	QArray[QBit]	The qubits to apply the IDENTITY gate on.	required

U

U(
    theta: CReal,
    phi: CReal,
    lam: CReal,
    gam: CReal,
    target: QBit,
) -> None

[Qmod core-library function]

Performs a general single-qubit unitary gate that applies phase and rotation with three Euler angles on a qubit.

This operation is represented by the following matrix:

\[ U(\theta, \phi, \lambda, \gamma) = e^{i \gamma} \begin{bmatrix} cos(\theta/2) & -e^{i(\lambda)} sin(\theta/2) \\ e^{i\phi} sin(\theta/2) & e^{i(\phi + \lambda)} cos(\theta/2) \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
theta	CReal	The first Euler angle in radians.	required
phi	CReal	The second Euler angle in radians.	required
lam	CReal	The third Euler angle in radians.	required
gam	CReal	The global phase angle in radians.	required
target	QBit	The qubit to apply the general single-qubit unitary gate to.	required

CCX

CCX(ctrl: QArray[QBit, Literal[2]], target: QBit) -> None

[Qmod core-library function]

Applies the Pauli-X gate to the target qubit, conditioned on the two control qubits (Toffoli).

This operation is represented by the following matrix:

\[ CCX = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \end{bmatrix} \]

Parameters:

Name	Type	Description	Default
ctrl	QArray[QBit, Literal[2]]	The control qubits.	required
target	QBit	The qubit to apply the conditioned Pauli-X gate on.	required