p.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.

"""Phase Gate."""

from __future__ import annotations
from cmath import exp
import numpy
from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.parameterexpression import ParameterValueType


class PhaseGate(Gate):
    r"""Single-qubit rotation about the Z axis.

    This is a diagonal gate. It can be implemented virtually in hardware
    via framechanges (i.e. at zero error and duration).

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

    **Circuit symbol:**

    .. parsed-literal::

             ┌──────┐
        q_0: ┤ P(λ) ├
             └──────┘

    **Matrix Representation:**

    .. math::

        P(\lambda) =
            \begin{pmatrix}
                1 & 0 \\
                0 & e^{i\lambda}
            \end{pmatrix}

    **Examples:**

        .. math::

            P(\lambda = \pi) = Z

        .. math::

            P(\lambda = \pi/2) = S

        .. math::

            P(\lambda = \pi/4) = T

    .. seealso::

        :class:`~qiskit.circuit.library.standard_gates.RZGate`:
        This gate is equivalent to RZ up to a phase factor.

            .. math::

                P(\lambda) = e^{i{\lambda}/2} RZ(\lambda)

        Reference for virtual Z gate implementation:
        `1612.00858 <https://arxiv.org/abs/1612.00858>`_
    """

    def __init__(
        self, theta: ParameterValueType, label: str | None = None, *, duration=None, unit="dt"
    ):
        """Create new Phase gate."""
        super().__init__("p", 1, [theta], label=label, duration=duration, unit=unit)

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

        q = QuantumRegister(1, "q")
        qc = QuantumCircuit(q, name=self.name)
        qc.append(UGate(0, 0, self.params[0]), [0])
        self.definition = qc

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

        Args:
            num_ctrl_qubits (int): number of control qubits.
            label (str or None): An optional label for the gate [Default: None]
            ctrl_state (int or str or None): 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 = CPhaseGate(self.params[0], label=label, ctrl_state=ctrl_state)
            gate.base_gate.label = self.label
        elif not annotated and ctrl_state is None and num_ctrl_qubits > 1:
            gate = MCPhaseGate(self.params[0], num_ctrl_qubits, label=label)
            gate.base_gate.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):
        r"""Return inverted Phase gate (:math:`Phase(\lambda)^{\dagger} = Phase(-\lambda)`)"""
        return PhaseGate(-self.params[0])

    def __array__(self, dtype=None):
        """Return a numpy.array for the Phase gate."""
        lam = float(self.params[0])
        return numpy.array([[1, 0], [0, exp(1j * lam)]], dtype=dtype)

    def power(self, exponent: float):
        """Raise gate to a power."""
        (theta,) = self.params
        return PhaseGate(exponent * theta)

    def __eq__(self, other):
        if isinstance(other, PhaseGate):
            return self._compare_parameters(other)
        return False


class CPhaseGate(ControlledGate):
    r"""Controlled-Phase gate.

    This is a diagonal and symmetric gate that induces a
    phase on the state of the target qubit, depending on the control state.

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

    **Circuit symbol:**

    .. parsed-literal::


        q_0: ─■──
              │λ
        q_1: ─■──


    **Matrix representation:**

    .. math::

        CPhase =
            I \otimes |0\rangle\langle 0| + P \otimes |1\rangle\langle 1| =
            \begin{pmatrix}
                1 & 0 & 0 & 0 \\
                0 & 1 & 0 & 0 \\
                0 & 0 & 1 & 0 \\
                0 & 0 & 0 & e^{i\lambda}
            \end{pmatrix}

    .. seealso::

        :class:`~qiskit.circuit.library.standard_gates.CRZGate`:
        Due to the global phase difference in the matrix definitions
        of Phase and RZ, CPhase and CRZ are different gates with a relative
        phase difference.
    """

    def __init__(
        self,
        theta: ParameterValueType,
        label: str | None = None,
        ctrl_state: str | int | None = None,
        *,
        duration=None,
        unit="dt",
        _base_label=None,
    ):
        """Create new CPhase gate."""
        super().__init__(
            "cp",
            2,
            [theta],
            num_ctrl_qubits=1,
            label=label,
            ctrl_state=ctrl_state,
            base_gate=PhaseGate(theta, label=_base_label),
            duration=duration,
            unit=unit,
        )

    def _define(self):
        """
        gate cphase(lambda) a,b
        { phase(lambda/2) a; cx a,b;
          phase(-lambda/2) b; cx a,b;
          phase(lambda/2) b;
        }
        """
        # pylint: disable=cyclic-import
        from qiskit.circuit.quantumcircuit import QuantumCircuit

        #      ┌────────┐
        # q_0: ┤ P(λ/2) ├──■───────────────■────────────
        #      └────────┘┌─┴─┐┌─────────┐┌─┴─┐┌────────┐
        # q_1: ──────────┤ X ├┤ P(-λ/2) ├┤ X ├┤ P(λ/2) ├
        #                └───┘└─────────┘└───┘└────────┘
        q = QuantumRegister(2, "q")
        qc = QuantumCircuit(q, name=self.name)
        qc.p(self.params[0] / 2, 0)
        qc.cx(0, 1)
        qc.p(-self.params[0] / 2, 1)
        qc.cx(0, 1)
        qc.p(self.params[0] / 2, 1)
        self.definition = qc

    def control(
        self,
        num_ctrl_qubits: int = 1,
        label: str | None = None,
        ctrl_state: str | int | None = None,
        annotated: bool = False,
    ):
        """Controlled version of this gate.

        Args:
            num_ctrl_qubits (int): number of control qubits.
            label (str or None): An optional label for the gate [Default: None]
            ctrl_state (int or str or None): 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 ctrl_state is None:
            gate = MCPhaseGate(self.params[0], num_ctrl_qubits=num_ctrl_qubits + 1, label=label)
            gate.base_gate.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):
        r"""Return inverted CPhase gate (:math:`CPhase(\lambda)^{\dagger} = CPhase(-\lambda)`)"""
        return CPhaseGate(-self.params[0], ctrl_state=self.ctrl_state)

    def __array__(self, dtype=None):
        """Return a numpy.array for the CPhase gate."""
        eith = exp(1j * float(self.params[0]))
        if self.ctrl_state:
            return numpy.array(
                [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, eith]], dtype=dtype
            )
        return numpy.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, eith, 0], [0, 0, 0, 1]], dtype=dtype)

    def power(self, exponent: float):
        """Raise gate to a power."""
        (theta,) = self.params
        return CPhaseGate(exponent * theta)

    def __eq__(self, other):
        if isinstance(other, CPhaseGate):
            return self._compare_parameters(other) and self.ctrl_state == other.ctrl_state
        return False


class MCPhaseGate(ControlledGate):
    r"""Multi-controlled-Phase gate.

    This is a diagonal and symmetric gate that induces a
    phase on the state of the target qubit, depending on the state of the control qubits.

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

    **Circuit symbol:**

    .. parsed-literal::

            q_0: ───■────
                    │
                    .
                    │
        q_(n-1): ───■────
                 ┌──┴───┐
            q_n: ┤ P(λ) ├
                 └──────┘

    .. seealso::

        :class:`~qiskit.circuit.library.standard_gates.CPhaseGate`:
        The singly-controlled-version of this gate.
    """

    def __init__(
        self,
        lam: ParameterValueType,
        num_ctrl_qubits: int,
        label: str | None = None,
        *,
        duration=None,
        unit="dt",
        _base_label=None,
    ):
        """Create new MCPhase gate."""
        super().__init__(
            "mcphase",
            num_ctrl_qubits + 1,
            [lam],
            num_ctrl_qubits=num_ctrl_qubits,
            label=label,
            base_gate=PhaseGate(lam, label=_base_label),
            duration=duration,
            unit=unit,
        )

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

        q = QuantumRegister(self.num_qubits, "q")
        qc = QuantumCircuit(q, name=self.name)

        if self.num_ctrl_qubits == 0:
            qc.p(self.params[0], 0)
        if self.num_ctrl_qubits == 1:
            qc.cp(self.params[0], 0, 1)
        else:
            from .u3 import _gray_code_chain

            scaled_lam = self.params[0] / (2 ** (self.num_ctrl_qubits - 1))
            bottom_gate = CPhaseGate(scaled_lam)
            for operation, qubits, clbits in _gray_code_chain(q, self.num_ctrl_qubits, bottom_gate):
                qc._append(operation, qubits, clbits)
        self.definition = qc

    def control(
        self,
        num_ctrl_qubits: int = 1,
        label: str | None = None,
        ctrl_state: str | int | None = None,
        annotated: bool = False,
    ):
        """Controlled version of this gate.

        Args:
            num_ctrl_qubits (int): number of control qubits.
            label (str or None): An optional label for the gate [Default: None]
            ctrl_state (int or str or None): 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 ctrl_state is None:
            gate = MCPhaseGate(
                self.params[0],
                num_ctrl_qubits=num_ctrl_qubits + self.num_ctrl_qubits,
                label=label,
            )
            gate.base_gate.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):
        r"""Return inverted MCU1 gate (:math:`MCU1(\lambda)^{\dagger} = MCU1(-\lambda)`)"""
        return MCPhaseGate(-self.params[0], self.num_ctrl_qubits)