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Extend Clifford class docs (backport #12177) #12301

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Apr 26, 2024
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Extend Clifford class docs (backport #12177) #12301

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20 changes: 18 additions & 2 deletions qiskit/quantum_info/operators/symplectic/clifford.py
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Expand Up @@ -38,7 +38,23 @@


class Clifford(BaseOperator, AdjointMixin, Operation):
"""An N-qubit unitary operator from the Clifford group.
r"""
An N-qubit unitary operator from the Clifford group.

An N-qubit Clifford operator takes Paulis to Paulis via conjugation
(up to a global phase). More precisely, the Clifford group :math:`\mathcal{C}_N`
is defined as

.. math::

\mathcal{C}_N = \{ U \in U(2^N) | U \mathcal{P}_N U^{\dagger} = \mathcal{P}_N \} / U(1)

where :math:`\mathcal{P}_N` is the Pauli group on :math:`N` qubits
that is generated by single-qubit Pauli operators,
and :math:`U` is a unitary operator in the unitary group
:math:`U(2^N)` representing operations on :math:`N` qubits.
:math:`\mathcal{C}_N` is the quotient group by the subgroup of
scalar unitary matrices :math:`U(1)`.

**Representation**

Expand Down Expand Up @@ -92,7 +108,7 @@ class Clifford(BaseOperator, AdjointMixin, Operation):
:class:`~qiskit.circuit.library.SGate`, :class:`~qiskit.circuit.library.SdgGate`,
:class:`~qiskit.circuit.library.SXGate`, :class:`~qiskit.circuit.library.SXdgGate`,
:class:`~qiskit.circuit.library.CXGate`, :class:`~qiskit.circuit.library.CZGate`,
:class:`~qiskit.circuit.library.CYGate`, :class:`~qiskit.circuit.library.DXGate`,
:class:`~qiskit.circuit.library.CYGate`, :class:`~qiskit.circuit.library.DCXGate`,
:class:`~qiskit.circuit.library.SwapGate`, :class:`~qiskit.circuit.library.iSwapGate`,
:class:`~qiskit.circuit.library.ECRGate`, :class:`~qiskit.circuit.library.LinearFunction`,
:class:`~qiskit.circuit.library.PermutationGate`.
Expand Down
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