pprop.gates.simpleclifford module

This submodule defines SimpleClifford, the base class for single-qubit Clifford gates, and the concrete gates H and S.

class pprop.gates.simpleclifford.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.simpleclifford.Hadamard

Alias for H.

class pprop.gates.simpleclifford.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.simpleclifford.SimpleClifford(wires, qml_gate, parameter, rule)[source]

Bases: Gate

Base class for single-qubit non-parametrised Clifford gates.

Clifford gates map every Pauli word to exactly one Pauli word, possibly with a sign flip. This is captured by a rule dict that maps each single-qubit Pauli label to an (output_label, sign) pair. Labels absent from the dict commute with the gate and pass through unchanged.

Parameters:

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

  • qml_gate (pennylane.operation.Operator) – Corresponding PennyLane gate class, used for circuit drawing.

  • parameter (int or None) – Clifford gates are non-parametrised, so this is always None.

  • rule (EvolutionRule) – Dict mapping a single-qubit Pauli label ("X", "Y", or "Z") to a (output_label, sign) tuple where sign is +1 or -1.

rule

The Heisenberg evolution rule for this gate.

Type:

EvolutionRule

evolve(word, k1, k2)[source]

Heisenberg-evolve a Pauli word through this Clifford gate.

Looks up the single-qubit Pauli at the gate’s wire in self.rule. If no rule exists the word commutes with the gate and is returned unchanged. Otherwise the qubit at that wire is replaced with the output label and all scalar coefficients are multiplied by the sign.

Parameters:

  • word (tuple[PauliOp, CoeffTerms]) – (pauliop, coeff_terms) pair to evolve.

  • k1 (int or None) – Pauli weight cutoff (unused, Clifford gates do not change weight).

  • k2 (int or None) – Frequency cutoff (unused, Clifford gates do not change frequency).

Returns:

A PauliDict with exactly one entry.

Return type:

PauliDict