qiskit/circuit/library/standard_gates/y.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.

"""Y and CY gates."""

from math import pi
from typing import Optional, Union

# pylint: disable=cyclic-import
from qiskit.circuit.singleton import SingletonGate, SingletonControlledGate, stdlib_singleton_key
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit._utils import with_gate_array, with_controlled_gate_array

_Y_ARRAY = [[0, -1j], [1j, 0]]


@with_gate_array(_Y_ARRAY)
class YGate(SingletonGate):
    r"""The single-qubit Pauli-Y gate (:math:`\sigma_y`).

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

    **Matrix Representation:**

    .. math::

        Y = \begin{pmatrix}
                0 & -i \\
                i & 0
            \end{pmatrix}

    **Circuit symbol:**

    .. parsed-literal::

             ┌───┐
        q_0: ┤ Y ├
             └───┘

    Equivalent to a :math:`\pi` radian rotation about the Y axis.

    .. note::

        A global phase difference exists between the definitions of
        :math:`RY(\pi)` and :math:`Y`.

        .. math::

            RY(\pi) = \begin{pmatrix}
                        0 & -1 \\
                        1 & 0
                      \end{pmatrix}
                    = -i Y

    The gate is equivalent to a bit and phase flip.

    .. math::

        |0\rangle \rightarrow i|1\rangle \\
        |1\rangle \rightarrow -i|0\rangle
    """

    def __init__(self, label: Optional[str] = None, *, duration=None, unit="dt"):
        """Create new Y gate."""
        super().__init__("y", 1, [], label=label, duration=duration, unit=unit)

    _singleton_lookup_key = stdlib_singleton_key()

    def _define(self):
        # pylint: disable=cyclic-import
        from qiskit.circuit.quantumcircuit import QuantumCircuit
        from .u3 import U3Gate

        q = QuantumRegister(1, "q")
        qc = QuantumCircuit(q, name=self.name)
        rules = [(U3Gate(pi, pi / 2, pi / 2), [q[0]], [])]
        for instr, qargs, cargs in rules:
            qc._append(instr, qargs, cargs)

        self.definition = qc

    def control(
        self,
        num_ctrl_qubits: int = 1,
        label: Optional[str] = None,
        ctrl_state: Optional[Union[str, int]] = None,
        annotated: bool = False,
    ):
        """Return a (multi-)controlled-Y gate.

        One control returns a CY 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 can be implemented
                as an annotated gate.

        Returns:
            ControlledGate: controlled version of this gate.
        """
        if not annotated and num_ctrl_qubits == 1:
            gate = CYGate(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):
        r"""Return inverted Y gate (:math:`Y^{\dagger} = Y`)

        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:
            YGate: inverse gate (self-inverse).
        """
        return YGate()  # self-inverse

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


@with_controlled_gate_array(_Y_ARRAY, num_ctrl_qubits=1)
class CYGate(SingletonControlledGate):
    r"""Controlled-Y gate.

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

    **Circuit symbol:**

    .. parsed-literal::

        q_0: ──■──
             ┌─┴─┐
        q_1: ┤ Y ├
             └───┘

    **Matrix representation:**

    .. math::

        CY\ q_0, q_1 =
        I \otimes |0 \rangle\langle 0| + Y \otimes |1 \rangle\langle 1|  =
            \begin{pmatrix}
                1 & 0 & 0 & 0 \\
                0 & 0 & 0 & -i \\
                0 & 0 & 1 & 0 \\
                0 & i & 0 & 0
            \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_1. Thus a textbook matrix for this
        gate will be:

        .. parsed-literal::
                 ┌───┐
            q_0: ┤ Y ├
                 └─┬─┘
            q_1: ──■──

        .. math::

            CY\ q_1, q_0 =
                |0 \rangle\langle 0| \otimes I + |1 \rangle\langle 1| \otimes Y =
                \begin{pmatrix}
                    1 & 0 & 0 & 0 \\
                    0 & 1 & 0 & 0 \\
                    0 & 0 & 0 & -i \\
                    0 & 0 & i & 0
                \end{pmatrix}

    """

    def __init__(
        self,
        label: Optional[str] = None,
        ctrl_state: Optional[Union[str, int]] = None,
        *,
        duration=None,
        unit="dt",
        _base_label=None,
    ):
        """Create new CY gate."""
        super().__init__(
            "cy",
            2,
            [],
            num_ctrl_qubits=1,
            label=label,
            ctrl_state=ctrl_state,
            base_gate=YGate(label=_base_label),
            duration=duration,
            unit=unit,
        )

    _singleton_lookup_key = stdlib_singleton_key(num_ctrl_qubits=1)

    def _define(self):
        """
        gate cy a,b { sdg b; cx a,b; s b; }
        """
        # pylint: disable=cyclic-import
        from qiskit.circuit.quantumcircuit import QuantumCircuit
        from .s import SGate, SdgGate
        from .x import CXGate

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

        self.definition = qc

    def inverse(self, annotated: bool = False):
        """Return inverted CY 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:
            CYGate: inverse gate (self-inverse).
        """
        return CYGate(ctrl_state=self.ctrl_state)  # self-inverse

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