# 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.

"""The S, Sdg, CS and CSdg gates."""

from math import pi
from typing import Optional, Union

import numpy

from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.library.standard_gates.p import CPhaseGate, PhaseGate
from qiskit.circuit.quantumregister import QuantumRegister


class SGate(Gate):
    r"""Single qubit S gate (Z**0.5).

    It induces a :math:`\pi/2` phase, and is sometimes called the P gate (phase).

    This is a Clifford gate and a square-root of Pauli-Z.

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

    **Matrix Representation:**

    .. math::

        S = \begin{pmatrix}
                1 & 0 \\
                0 & i
            \end{pmatrix}

    **Circuit symbol:**

    .. parsed-literal::

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

    Equivalent to a :math:`\pi/2` radian rotation about the Z axis.
    """

    def __init__(self, label: Optional[str] = None):
        """Create new S gate."""
        super().__init__("s", 1, [], label=label)

    def _define(self):
        """
        gate s a { u1(pi/2) a; }
        """
        # pylint: disable=cyclic-import
        from qiskit.circuit.quantumcircuit import QuantumCircuit

        from .u1 import U1Gate

        q = QuantumRegister(1, "q")
        qc = QuantumCircuit(q, name=self.name)
        rules = [(U1Gate(pi / 2), [q[0]], [])]
        for instr, qargs, cargs in rules:
            qc._append(instr, qargs, cargs)

        self.definition = qc

    def inverse(self):
        """Return inverse of S (SdgGate)."""
        return SdgGate()

    def __array__(self, dtype=None):
        """Return a numpy.array for the S gate."""
        return numpy.array([[1, 0], [0, 1j]], dtype=dtype)

    def power(self, exponent: float):
        """Raise gate to a power."""
        return PhaseGate(0.5 * numpy.pi * exponent)


class SdgGate(Gate):
    r"""Single qubit S-adjoint gate (~Z**0.5).

    It induces a :math:`-\pi/2` phase.

    This is a Clifford gate and a square-root of Pauli-Z.

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

    **Matrix Representation:**

    .. math::

        Sdg = \begin{pmatrix}
                1 & 0 \\
                0 & -i
            \end{pmatrix}

    **Circuit symbol:**

    .. parsed-literal::

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

    Equivalent to a :math:`-\pi/2` radian rotation about the Z axis.
    """

    def __init__(self, label: Optional[str] = None):
        """Create new Sdg gate."""
        super().__init__("sdg", 1, [], label=label)

    def _define(self):
        """
        gate sdg a { u1(-pi/2) a; }
        """
        # pylint: disable=cyclic-import
        from qiskit.circuit.quantumcircuit import QuantumCircuit

        from .u1 import U1Gate

        q = QuantumRegister(1, "q")
        qc = QuantumCircuit(q, name=self.name)
        rules = [(U1Gate(-pi / 2), [q[0]], [])]
        for instr, qargs, cargs in rules:
            qc._append(instr, qargs, cargs)

        self.definition = qc

    def inverse(self):
        """Return inverse of Sdg (SGate)."""
        return SGate()

    def __array__(self, dtype=None):
        """Return a numpy.array for the Sdg gate."""
        return numpy.array([[1, 0], [0, -1j]], dtype=dtype)

    def power(self, exponent: float):
        """Raise gate to a power."""
        return PhaseGate(-0.5 * numpy.pi * exponent)


class CSGate(ControlledGate):
    r"""Controlled-S gate.

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

    **Circuit symbol:**

    .. parsed-literal::

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

    **Matrix representation:**

    .. math::

        CS \ q_0, q_1 =
        I \otimes |0 \rangle\langle 0| + S \otimes |1 \rangle\langle 1|  =
            \begin{pmatrix}
                1 & 0 & 0 & 0 \\
                0 & 1 & 0 & 0 \\
                0 & 0 & 1 & 0 \\
                0 & 0 & 0 & i
            \end{pmatrix}
    """
    # Define class constants. This saves future allocation time.
    _matrix1 = numpy.array(
        [
            [1, 0, 0, 0],
            [0, 1, 0, 0],
            [0, 0, 1, 0],
            [0, 0, 0, 1j],
        ]
    )
    _matrix0 = numpy.array(
        [
            [1, 0, 0, 0],
            [0, 1, 0, 0],
            [0, 0, 1j, 0],
            [0, 0, 0, 1],
        ]
    )

    def __init__(self, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None):
        """Create new CS gate."""
        super().__init__(
            "cs", 2, [], label=label, num_ctrl_qubits=1, ctrl_state=ctrl_state, base_gate=SGate()
        )

    def _define(self):
        """
        gate cs a,b { h b; cp(pi/2) a,b; h b; }
        """
        self.definition = CPhaseGate(theta=pi / 2).definition

    def inverse(self):
        """Return inverse of CSGate (CSdgGate)."""
        return CSdgGate(ctrl_state=self.ctrl_state)

    def __array__(self, dtype=None):
        """Return a numpy.array for the CS gate."""
        mat = self._matrix1 if self.ctrl_state == 1 else self._matrix0
        if dtype is not None:
            return numpy.asarray(mat, dtype=dtype)
        return mat

    def power(self, exponent: float):
        """Raise gate to a power."""
        return CPhaseGate(0.5 * numpy.pi * exponent)


class CSdgGate(ControlledGate):
    r"""Controlled-S^\dagger gate.

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

    **Circuit symbol:**

    .. parsed-literal::

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

    **Matrix representation:**

    .. math::

        CS^\dagger \ q_0, q_1 =
        I \otimes |0 \rangle\langle 0| + S^\dagger \otimes |1 \rangle\langle 1|  =
            \begin{pmatrix}
                1 & 0 & 0 & 0 \\
                0 & 1 & 0 & 0 \\
                0 & 0 & 1 & 0 \\
                0 & 0 & 0 & -i
            \end{pmatrix}
    """
    # Define class constants. This saves future allocation time.
    _matrix1 = numpy.array(
        [
            [1, 0, 0, 0],
            [0, 1, 0, 0],
            [0, 0, 1, 0],
            [0, 0, 0, -1j],
        ]
    )
    _matrix0 = numpy.array(
        [
            [1, 0, 0, 0],
            [0, 1, 0, 0],
            [0, 0, -1j, 0],
            [0, 0, 0, 1],
        ]
    )

    def __init__(self, label: Optional[str] = None, ctrl_state: Optional[Union[str, int]] = None):
        """Create new CSdg gate."""
        super().__init__(
            "csdg",
            2,
            [],
            label=label,
            num_ctrl_qubits=1,
            ctrl_state=ctrl_state,
            base_gate=SdgGate(),
        )

    def _define(self):
        """
        gate csdg a,b { h b; cp(-pi/2) a,b; h b; }
        """
        self.definition = CPhaseGate(theta=-pi / 2).definition

    def inverse(self):
        """Return inverse of CSdgGate (CSGate)."""
        return CSGate(ctrl_state=self.ctrl_state)

    def __array__(self, dtype=None):
        """Return a numpy.array for the CSdg gate."""
        mat = self._matrix1 if self.ctrl_state == 1 else self._matrix0
        if dtype is not None:
            return numpy.asarray(mat, dtype=dtype)
        return mat

    def power(self, exponent: float):
        """Raise gate to a power."""
        return CPhaseGate(-0.5 * numpy.pi * exponent)
