qiskit/circuit/library/standard_gates/swap.py

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""Swap gate."""

from __future__ import annotations

from typing import Optional, Union
import numpy
from qiskit.circuit.singleton import SingletonGate, SingletonControlledGate, stdlib_singleton_key
from qiskit.circuit._utils import with_gate_array, with_controlled_gate_array
from qiskit._accelerate.circuit import StandardGate


_SWAP_ARRAY = numpy.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])


@with_gate_array(_SWAP_ARRAY)
class SwapGate(SingletonGate):
    r"""The SWAP gate.

    This is a symmetric and Clifford gate.

    Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
    with the :meth:`~qiskit.circuit.QuantumCircuit.swap` method.

    **Circuit symbol:**

    .. code-block:: text

        q_0: ─X─
              │
        q_1: ─X─

    **Matrix Representation:**

    .. math::

        SWAP =
            \begin{pmatrix}
                1 & 0 & 0 & 0 \\
                0 & 0 & 1 & 0 \\
                0 & 1 & 0 & 0 \\
                0 & 0 & 0 & 1
            \end{pmatrix}

    The gate is equivalent to a state swap and is a classical logic gate.

    .. math::

        |a, b\rangle \rightarrow |b, a\rangle
    """

    _standard_gate = StandardGate.Swap

    def __init__(self, label: Optional[str] = None):
        """Create new SWAP gate."""
        super().__init__("swap", 2, [], label=label)

    _singleton_lookup_key = stdlib_singleton_key()

    def _define(self):
        """
        gate swap a,b { cx a,b; cx b,a; cx a,b; }
        """
        # pylint: disable=cyclic-import
        from qiskit.circuit import QuantumCircuit, QuantumRegister
        from .x import CXGate

        q = QuantumRegister(2, "q")
        qc = QuantumCircuit(q, name=self.name)
        rules = [
            (CXGate(), [q[0], q[1]], []),
            (CXGate(), [q[1], q[0]], []),
            (CXGate(), [q[0], q[1]], []),
        ]
        for instr, qargs, cargs in rules:
            qc._append(instr, qargs, cargs)

        self.definition = qc

    def control(
        self,
        num_ctrl_qubits: int = 1,
        label: str | None = None,
        ctrl_state: str | int | None = None,
        annotated: bool | None = None,
    ):
        """Return a (multi-)controlled-SWAP gate.

        One control returns a CSWAP (Fredkin) gate.

        Args:
            num_ctrl_qubits: number of control qubits.
            label: An optional label for the gate [Default: ``None``]
            ctrl_state: control state expressed as integer,
                string (e.g.``'110'``), or ``None``. If ``None``, use all 1s.
            annotated: indicates whether the controlled gate should be implemented
                as an annotated gate. If ``None``, this is handled as ``False``.

        Returns:
            ControlledGate: controlled version of this gate.
        """
        if not annotated and num_ctrl_qubits == 1:
            gate = CSwapGate(label=label, ctrl_state=ctrl_state, _base_label=self.label)
        else:
            gate = super().control(
                num_ctrl_qubits=num_ctrl_qubits,
                label=label,
                ctrl_state=ctrl_state,
                annotated=annotated,
            )
        return gate

    def inverse(self, annotated: bool = False):
        """Return inverse Swap gate (itself).

        Args:
            annotated: when set to ``True``, this is typically used to return an
                :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete
                :class:`.Gate`. However, for this class this argument is ignored as this gate
                is self-inverse.

        Returns:
            SwapGate: inverse gate (self-inverse).
        """
        return SwapGate()  # self-inverse

    def __eq__(self, other):
        return isinstance(other, SwapGate)


@with_controlled_gate_array(_SWAP_ARRAY, num_ctrl_qubits=1)
class CSwapGate(SingletonControlledGate):
    r"""Controlled-SWAP gate, also known as the Fredkin gate.

    Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
    with the :meth:`~qiskit.circuit.QuantumCircuit.cswap` and
    :meth:`~qiskit.circuit.QuantumCircuit.fredkin` methods.

    **Circuit symbol:**

    .. code-block:: text

        q_0: ─■─
              │
        q_1: ─X─
              │
        q_2: ─X─


    **Matrix representation:**

    .. math::

        CSWAP\ q_0, q_1, q_2 =
            I \otimes I \otimes |0 \rangle \langle 0| +
            SWAP \otimes |1 \rangle \langle 1| =
            \begin{pmatrix}
                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 & 0 & 1 & 0 & 0 \\
                0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
                0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
            \end{pmatrix}

    .. note::

        In Qiskit's convention, higher qubit indices are more significant
        (little endian convention). In many textbooks, controlled gates are
        presented with the assumption of more significant qubits as control,
        which in our case would be q_2. Thus a textbook matrix for this
        gate will be:

        .. code-block:: text

            q_0: ─X─
                  │
            q_1: ─X─
                  │
            q_2: ─■─

        .. math::

            CSWAP\ q_2, q_1, q_0 =
                |0 \rangle \langle 0| \otimes I \otimes I +
                |1 \rangle \langle 1| \otimes SWAP =
                \begin{pmatrix}
                    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 & 0 \\
                    0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
                \end{pmatrix}

    In the computational basis, this gate swaps the states of
    the two target qubits if the control qubit is in the
    :math:`|1\rangle` state.

    .. math::
        |0, b, c\rangle \rightarrow |0, b, c\rangle
        |1, b, c\rangle \rightarrow |1, c, b\rangle
    """

    _standard_gate = StandardGate.CSwap

    def __init__(
        self,
        label: Optional[str] = None,
        ctrl_state: Optional[Union[str, int]] = None,
        *,
        _base_label=None,
    ):
        """Create new CSWAP gate."""
        super().__init__(
            "cswap",
            3,
            [],
            num_ctrl_qubits=1,
            label=label,
            ctrl_state=ctrl_state,
            base_gate=SwapGate(label=_base_label),
        )

    _singleton_lookup_key = stdlib_singleton_key(num_ctrl_qubits=1)

    def _define(self):
        """
        gate cswap a,b,c
        { cx c,b;
          ccx a,b,c;
          cx c,b;
        }
        """
        # pylint: disable=cyclic-import
        from qiskit.circuit import QuantumCircuit, QuantumRegister
        from .x import CXGate, CCXGate

        q = QuantumRegister(3, "q")
        qc = QuantumCircuit(q, name=self.name)
        rules = [
            (CXGate(), [q[2], q[1]], []),
            (CCXGate(), [q[0], q[1], q[2]], []),
            (CXGate(), [q[2], q[1]], []),
        ]
        for instr, qargs, cargs in rules:
            qc._append(instr, qargs, cargs)

        self.definition = qc

    def inverse(self, annotated: bool = False):
        """Return inverse CSwap gate (itself).

        Args:
            annotated: when set to ``True``, this is typically used to return an
                :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete
                :class:`.Gate`. However, for this class this argument is ignored as this gate
                is self-inverse.

        Returns:
            CSwapGate: inverse gate (self-inverse).
        """
        return CSwapGate(ctrl_state=self.ctrl_state)  # self-inverse

    def __eq__(self, other):
        return isinstance(other, CSwapGate) and self.ctrl_state == other.ctrl_state