pprop.gates package

Submodules

Module contents

This module defines gate classes compatible with PennyLane

In submodules:
  • Single-qubit Clifford gates (clifford.py):

    • H: Hadamard

    • S: Phase gate

  • Single-qubit non-clifford gates (nonclifford.py):

    • T: T gate

  • Single-qubit parametrized gates (rotation.py):

    • RX, RY, RZ: Parametrized rotation gates

  • Controlled 2-Qubit gates (controlled.py):

    • CNOT, CY, CZ: Standard two-qubit gates

class pprop.gates.CNOT(wires, parameter=None)[source]

Bases: ControlledGate

The Controlled-NOT (CX) gate.

\[\begin{split}\text{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix}\end{split}\]

The Heisenberg evolution maps each two-qubit Pauli string control ⊗ target according to the rule dict. All other combinations commute with the gate.

Parameters:

  • wires (list[int]) – [control, target] qubit indices.

  • parameter (float, int, optional) – Unused. Defaults to None.

class pprop.gates.CRX(wires, parameter)[source]

Bases: ControlledRotationGate

The controlled-\(R_x\) gate.

\[\begin{split}CR_x(\theta) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\theta) & -i\sin(\theta) \\ 0 & 0 & -i\sin(\theta) & \cos(\theta) \end{bmatrix}\end{split}\]

Note

The parameter θ here corresponds to θ/2 in PennyLane’s convention. Pass params[i] / 2 to qml.CRX to match.

Parameters:

  • wires (list[int]) – [control, target] qubit indices.

  • parameter (int) – Index of \(\\theta\) in the global parameter vector.

class pprop.gates.CRY(wires, parameter)[source]

Bases: ControlledRotationGate

The controlled-\(R_y\) gate.

\[\begin{split}CR_y(\theta) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & \cos(\theta) & -\sin(\theta) \\ 0 & 0 & \sin(\theta) & \cos(\theta) \end{bmatrix}\end{split}\]

Note

The parameter θ here corresponds to θ/2 in PennyLane’s convention. Pass params[i] / 2 to qml.CRY to match.

Parameters:

  • wires (list[int]) – [control, target] qubit indices.

  • parameter (int) – Index of \(\\theta\) in the global parameter vector.

class pprop.gates.CRZ(wires, parameter)[source]

Bases: ControlledRotationGate

The controlled-\(R_z\) gate.

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

Note

The parameter θ here corresponds to θ/2 in PennyLane’s convention. Pass params[i] / 2 to qml.CRZ to match.

Parameters:

  • wires (list[int]) – [control, target] qubit indices.

  • parameter (int) – Index of \(\\theta\) in the global parameter vector.

class pprop.gates.CY(wires, parameter=None)[source]

Bases: ControlledGate

The Controlled-Y gate.

\[\begin{split}\text{CY} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & -i \\ 0 & 0 & i & 0 \end{bmatrix}\end{split}\]
Parameters:

  • wires (list[int]) – [control, target] qubit indices.

  • parameter (float, int, optional) – Unused. Defaults to None.

class pprop.gates.CZ(wires, parameter=None)[source]

Bases: ControlledGate

The Controlled-Z gate.

\[\begin{split}\text{CZ} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix}\end{split}\]
Parameters:

  • wires (list[int]) – [control, target] qubit indices.

  • parameter (float, int, optional) – Unused. Defaults to None.

class pprop.gates.H(wires, parameter=None)[source]

Bases: SimpleClifford

The single-qubit Hadamard gate.

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

Heisenberg evolution rules:

\[X \mapsto Z, \quad Y \mapsto -Y, \quad Z \mapsto X\]
Parameters:

  • wires (list[int]) – Qubit on which the gate acts.

  • parameter (float, int, optional) – Unused. Defaults to None.

pprop.gates.Hadamard

alias of H

class pprop.gates.RX(wires, parameter)[source]

Bases: RotationGate

The single-qubit parametrised X rotation gate.

\[R_x(\phi) = e^{-i\phi\,\sigma_x/2}\]

Heisenberg evolution rules:

\[Y \mapsto -\sin(\phi)\,Z + \cos(\phi)\,Y, \quad Z \mapsto +\sin(\phi)\,Y + \cos(\phi)\,Z, \quad X \mapsto X\]
Parameters:

  • wires (list[int]) – Qubit on which the gate acts.

  • parameter (int) – Index of \(\phi\) in the global parameter vector.

class pprop.gates.RY(wires, parameter)[source]

Bases: RotationGate

The single-qubit parametrised Y rotation gate.

\[R_y(\phi) = e^{-i\phi\,\sigma_y/2}\]

Heisenberg evolution rules:

\[X \mapsto +\sin(\phi)\,Z + \cos(\phi)\,X, \quad Z \mapsto -\sin(\phi)\,X + \cos(\phi)\,Z, \quad Y \mapsto Y\]
Parameters:

  • wires (list[int]) – Qubit on which the gate acts.

  • parameter (int) – Index of \(\phi\) in the global parameter vector.

class pprop.gates.RZ(wires, parameter)[source]

Bases: RotationGate

The single-qubit parametrised Z rotation gate.

\[R_z(\phi) = e^{-i\phi\,\sigma_z/2}\]

Heisenberg evolution rules:

\[X \mapsto -\sin(\phi)\,Y + \cos(\phi)\,X, \quad Y \mapsto +\sin(\phi)\,X + \cos(\phi)\,Y, \quad Z \mapsto Z\]
Parameters:

  • wires (list[int]) – Qubit on which the gate acts.

  • parameter (int) – Index of \(\phi\) in the global parameter vector.

class pprop.gates.S(wires, parameter=None)[source]

Bases: SimpleClifford

The single-qubit phase gate.

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

Heisenberg evolution rules:

\[X \mapsto -Y, \quad Y \mapsto X, \quad Z \mapsto Z\]
Parameters:

  • wires (list[int]) – Qubit on which the gate acts.

  • parameter (float, int, optional) – Unused. Defaults to None.

class pprop.gates.T(wires, parameter=None)[source]

Bases: SimpleNonClifford

The single-qubit T gate.

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

The Heisenberg evolution rules are:

\[ \begin{align}\begin{aligned}X \;\mapsto\; \tfrac{1}{\sqrt{2}} X - \tfrac{1}{\sqrt{2}} Y\\Y \;\mapsto\; \tfrac{1}{\sqrt{2}} Y + \tfrac{1}{\sqrt{2}} X\\Z \;\mapsto\; Z\end{aligned}\end{align} \]
Parameters:

  • wires (list[int]) – Qubit on which the gate acts.

  • parameter (float, int, optional) – Unused for non-parametrised gates. Defaults to None.