Standard Gates

Functions:

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:

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:

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:

Z

Z(
target: Const[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:

I

I(
target: Const[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:

S

S(
target: Const[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:

T

T(
target: Const[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:

SDG

SDG(
target: Const[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:

TDG

TDG(
target: Const[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:

PHASE

PHASE(
theta: CReal,
target: Const[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:

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:

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:

RZ

RZ(
theta: CReal,
target: Const[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:

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:

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:

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:

RZZ

RZZ(
theta: CReal,
target: Const[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:

CH

CH(
ctrl: Const[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:

CX

CX(
ctrl: Const[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:

CY

CY(
ctrl: Const[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:

CZ

CZ(
ctrl: Const[QBit],
target: Const[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:

CRX

CRX(
theta: CReal,
ctrl: Const[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:

CRY

CRY(
theta: CReal,
ctrl: Const[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:

CRZ

CRZ(
theta: CReal,
ctrl: Const[QBit],
target: Const[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:

CPHASE

CPHASE(
theta: CReal,
ctrl: Const[QBit],
target: Const[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:

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:

IDENTITY

IDENTITY(
target: Const[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:

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:

CCX

CCX(
ctrl: Const[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: