Source code for pennylane.ops.qubit.non_parametric_ops

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at

#     http://www.apache.org/licenses/LICENSE-2.0

# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
This submodule contains the discrete-variable quantum operations that do
not depend on any parameters.
"""
# pylint:disable=abstract-method,arguments-differ,protected-access,invalid-overridden-method, no-member
import cmath
from copy import copy
from functools import lru_cache
from typing import Optional, Union

import numpy as np
from scipy import sparse

import pennylane as qml
from pennylane.decomposition import add_decomps, register_resources
from pennylane.operation import Observable, Operation
from pennylane.typing import TensorLike
from pennylane.wires import Wires, WiresLike

INV_SQRT2 = 1 / qml.math.sqrt(2)


class Hadamard(Observable, Operation):
    r"""Hadamard(wires)
    The Hadamard operator

    .. math:: H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1\\ 1 & -1\end{bmatrix}.

    .. seealso:: The equivalent short-form alias :class:`~H`

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    """int: Number of wires that the operator acts on."""

    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    resource_keys = set()

    _queue_category = "_ops"

    def __init__(self, wires: WiresLike, id: Optional[str] = None):
        super().__init__(wires=wires, id=id)

    def label(
        self,
        decimals: Optional[int] = None,
        base_label: Optional[str] = None,
        cache: Optional[dict] = None,
    ) -> str:
        return base_label or "H"

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"H('{wire}')"
        return f"H({wire})"

    @property
    def name(self) -> str:
        return "Hadamard"

    @property
    def resource_params(self) -> dict:
        return {}

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.Hadamard.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.Hadamard.compute_matrix())
        [[ 0.70710678  0.70710678]
         [ 0.70710678 -0.70710678]]
        """
        return np.array([[INV_SQRT2, INV_SQRT2], [INV_SQRT2, -INV_SQRT2]])

    @staticmethod
    @lru_cache()
    def compute_sparse_matrix(format="csr") -> sparse.spmatrix:  # pylint: disable=arguments-differ
        return sparse.csr_matrix([[INV_SQRT2, INV_SQRT2], [INV_SQRT2, -INV_SQRT2]]).asformat(
            format=format
        )

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.Hadamard.eigvals`

        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.Hadamard.compute_eigvals())
        [ 1 -1]
        """
        return qml.pauli.pauli_eigs(1)

    @staticmethod
    def compute_diagonalizing_gates(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Sequence of gates that diagonalize the operator in the computational basis (static method).

        Given the eigendecomposition :math:`O = U \Sigma U^{\dagger}` where
        :math:`\Sigma` is a diagonal matrix containing the eigenvalues,
        the sequence of diagonalizing gates implements the unitary :math:`U^{\dagger}`.

        The diagonalizing gates rotate the state into the eigenbasis
        of the operator.

        .. seealso:: :meth:`~.Hadamard.diagonalizing_gates`.

        Args:
            wires (Iterable[Any], Wires): wires that the operator acts on
        Returns:
            list[.Operator]: list of diagonalizing gates

        **Example**

        >>> print(qml.Hadamard.compute_diagonalizing_gates(wires=[0]))
        [RY(-0.7853981633974483, wires=[0])]
        """
        return [qml.RY(-np.pi / 4, wires=wires)]

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.

        .. seealso:: :meth:`~.Hadamard.decomposition`.

        Args:
            wires (Any, Wires): Wire that the operator acts on.

        Returns:
            list[Operator]: decomposition of the operator

        **Example:**

        >>> print(qml.Hadamard.compute_decomposition(0))
        [PhaseShift(1.5707963267948966, wires=[0]),
        RX(1.5707963267948966, wires=[0]),
        PhaseShift(1.5707963267948966, wires=[0])]

        """
        return [
            qml.PhaseShift(np.pi / 2, wires=wires),
            qml.RX(np.pi / 2, wires=wires),
            qml.PhaseShift(np.pi / 2, wires=wires),
        ]

    def _controlled(self, wire: WiresLike) -> "qml.CH":
        return qml.CH(wires=Wires(wire) + self.wires)

    def adjoint(self) -> "Hadamard":
        return Hadamard(wires=self.wires)

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # H = RZ(\pi) RY(\pi/2) RZ(0)
        return [np.pi, np.pi / 2, 0.0]

    def pow(self, z: Union[int, float]):
        return super().pow(z % 2)


def _hadamard_rz_rx_resources():
    return {qml.RZ: 2, qml.RX: 1, qml.GlobalPhase: 1}


@register_resources(_hadamard_rz_rx_resources)
def _hadamard_to_rz_rx(wires: WiresLike, **__):
    qml.RZ(np.pi / 2, wires=wires)
    qml.RX(np.pi / 2, wires=wires)
    qml.RZ(np.pi / 2, wires=wires)
    qml.GlobalPhase(-np.pi / 2, wires=wires)


def _hadamard_rz_ry_resources():
    return {qml.RZ: 1, qml.RY: 1, qml.GlobalPhase: 1}


@register_resources(_hadamard_rz_ry_resources)
def _hadamard_to_rz_ry(wires: WiresLike, **__):
    qml.RZ(np.pi, wires=wires)
    qml.RY(np.pi / 2, wires=wires)
    qml.GlobalPhase(-np.pi / 2)


add_decomps(Hadamard, _hadamard_to_rz_rx, _hadamard_to_rz_ry)

H = Hadamard
r"""H(wires)
The Hadamard operator

.. math:: H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1\\ 1 & -1\end{bmatrix}.

.. seealso:: The equivalent long-form alias :class:`~Hadamard`

**Details:**

* Number of wires: 1
* Number of parameters: 0

Args:
    wires (Sequence[int] or int): the wire the operation acts on
"""


class PauliX(Observable, Operation):
    r"""
    The Pauli X operator

    .. math:: \sigma_x = \begin{bmatrix} 0 & 1 \\ 1 & 0\end{bmatrix}.

    .. seealso:: The equivalent short-form alias :class:`~X`

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    """int: Number of wires that the operator acts on."""

    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    basis = "X"

    resource_keys = set()

    batch_size = None

    resource_keys = set()

    _queue_category = "_ops"

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {qml.pauli.PauliWord({self.wires[0]: "X"}): 1.0}
            )
        return self._pauli_rep

    def __init__(self, wires: WiresLike, id: Optional[str] = None):
        super().__init__(wires=wires, id=id)

    def label(
        self,
        decimals: Optional[int] = None,
        base_label: Optional[str] = None,
        cache: Optional[dict] = None,
    ) -> str:
        return base_label or "X"

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"X('{wire}')"
        return f"X({wire})"

    @property
    def name(self) -> str:
        return "PauliX"

    @property
    def resource_params(self) -> dict:
        return {}

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.X.matrix`


        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.X.compute_matrix())
        [[0 1]
         [1 0]]
        """
        return np.array([[0, 1], [1, 0]])

    @staticmethod
    @lru_cache()
    def compute_sparse_matrix(format="csr") -> sparse.spmatrix:  # pylint: disable=arguments-differ
        return sparse.csr_matrix([[0, 1], [1, 0]]).asformat(format=format)

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.X.eigvals`

        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.X.compute_eigvals())
        [ 1 -1]
        """
        return qml.pauli.pauli_eigs(1)

    @staticmethod
    def compute_diagonalizing_gates(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Sequence of gates that diagonalize the operator in the computational basis (static method).

        Given the eigendecomposition :math:`O = U \Sigma U^{\dagger}` where
        :math:`\Sigma` is a diagonal matrix containing the eigenvalues,
        the sequence of diagonalizing gates implements the unitary :math:`U^{\dagger}`.

        The diagonalizing gates rotate the state into the eigenbasis
        of the operator.

        .. seealso:: :meth:`~.X.diagonalizing_gates`.

        Args:
           wires (Iterable[Any], Wires): wires that the operator acts on
        Returns:
           list[.Operator]: list of diagonalizing gates

        **Example**

        >>> print(qml.X.compute_diagonalizing_gates(wires=[0]))
        [H(0)]
        """
        return [Hadamard(wires=wires)]

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.X.decomposition`.

        Args:
            wires (Any, Wires): Wire that the operator acts on.

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.X.compute_decomposition(0))
        [RX(3.141592653589793, wires=[0]),
        GlobalPhase(-1.5707963267948966, wires=[0])]

        """
        return [qml.RX(np.pi, wires=wires), qml.GlobalPhase(-np.pi / 2, wires=wires)]

    def adjoint(self) -> "PauliX":
        return X(wires=self.wires)

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        z_mod2 = z % 2
        if abs(z_mod2 - 0.5) < 1e-6:
            return [SX(wires=self.wires)]
        return super().pow(z_mod2)

    def _controlled(self, wire: WiresLike) -> "qml.CNOT":
        return qml.CNOT(wires=Wires(wire) + self.wires)

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # X = RZ(-\pi/2) RY(\pi) RZ(\pi/2)
        return [np.pi / 2, np.pi, -np.pi / 2]


X = PauliX
r"""The Pauli X operator

.. math:: \sigma_x = \begin{bmatrix} 0 & 1 \\ 1 & 0\end{bmatrix}.

.. seealso:: The equivalent long-form alias :class:`~PauliX`

**Details:**

* Number of wires: 1
* Number of parameters: 0

Args:
    wires (Sequence[int] or int): the wire the operation acts on
"""


def _paulix_to_rx_gp_resources():
    return {qml.GlobalPhase: 1, qml.RX: 1}


@register_resources(_paulix_to_rx_gp_resources)
def _paulix_to_rx_gp(wires: WiresLike, **__):
    qml.RX(np.pi, wires=wires)
    qml.GlobalPhase(-np.pi / 2, wires=wires)


add_decomps(PauliX, _paulix_to_rx_gp)


class PauliY(Observable, Operation):
    r"""
    The Pauli Y operator

    .. math:: \sigma_y = \begin{bmatrix} 0 & -i \\ i & 0\end{bmatrix}.

    .. seealso:: The equivalent short-form alias :class:`~Y`

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    """int: Number of wires that the operator acts on."""

    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    resource_keys = set()

    basis = "Y"

    batch_size = None

    _queue_category = "_ops"

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {qml.pauli.PauliWord({self.wires[0]: "Y"}): 1.0}
            )
        return self._pauli_rep

    def __init__(self, wires: WiresLike, id: Optional[str] = None):
        super().__init__(wires=wires, id=id)

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"Y('{wire}')"
        return f"Y({wire})"

    def label(
        self,
        decimals: Optional[int] = None,
        base_label: Optional[str] = None,
        cache: Optional[dict] = None,
    ) -> str:
        return base_label or "Y"

    @property
    def name(self) -> str:
        return "PauliY"

    @property
    def resource_params(self) -> dict:
        return {}

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.Y.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.Y.compute_matrix())
        [[ 0.+0.j -0.-1.j]
         [ 0.+1.j  0.+0.j]]
        """
        return np.array([[0, -1j], [1j, 0]])

    @staticmethod
    @lru_cache()
    def compute_sparse_matrix(format="csr") -> sparse.spmatrix:  # pylint: disable=arguments-differ
        return sparse.csr_matrix([[0, -1j], [1j, 0]]).asformat(format=format)

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.Y.eigvals`

        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.Y.compute_eigvals())
        [ 1 -1]
        """
        return qml.pauli.pauli_eigs(1)

    @staticmethod
    def compute_diagonalizing_gates(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Sequence of gates that diagonalize the operator in the computational basis (static method).

        Given the eigendecomposition :math:`O = U \Sigma U^{\dagger}` where
        :math:`\Sigma` is a diagonal matrix containing the eigenvalues,
        the sequence of diagonalizing gates implements the unitary :math:`U^{\dagger}`.

        The diagonalizing gates rotate the state into the eigenbasis
        of the operator.

        .. seealso:: :meth:`~.Y.diagonalizing_gates`.

        Args:
            wires (Iterable[Any], Wires): wires that the operator acts on
        Returns:
            list[.Operator]: list of diagonalizing gates

        **Example**

        >>> print(qml.Y.compute_diagonalizing_gates(wires=[0]))
        [Z(0), S(0), H(0)]
        """
        return [
            Z(wires=wires),
            S(wires=wires),
            Hadamard(wires=wires),
        ]

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.

        .. seealso:: :meth:`~.Y.decomposition`.

        Args:
            wires (Any, Wires): Single wire that the operator acts on.

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.Y.compute_decomposition(0))
        [RY(3.141592653589793, wires=[0]),
        GlobalPhase(-1.5707963267948966, wires=[0])]

        """
        return [qml.RY(np.pi, wires=wires), qml.GlobalPhase(-np.pi / 2, wires=wires)]

    def adjoint(self) -> "PauliY":
        return Y(wires=self.wires)

    def pow(self, z: Union[float, int]) -> list[qml.operation.Operator]:
        return super().pow(z % 2)

    def _controlled(self, wire: WiresLike) -> "qml.CY":
        return qml.CY(wires=Wires(wire) + self.wires)

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # Y = RZ(0) RY(\pi) RZ(0)
        return [0.0, np.pi, 0.0]


Y = PauliY
r"""The Pauli Y operator

.. math:: \sigma_y = \begin{bmatrix} 0 & -i \\ i & 0\end{bmatrix}.

.. seealso:: The equivalent long-form alias :class:`~PauliY`

**Details:**

* Number of wires: 1
* Number of parameters: 0

Args:
    wires (Sequence[int] or int): the wire the operation acts on
"""


def _pauliy_to_ry_gp_resources():
    return {qml.GlobalPhase: 1, qml.RY: 1}


@register_resources(_pauliy_to_ry_gp_resources)
def _pauliy_to_ry_gp(wires: WiresLike, **__):
    qml.RY(np.pi, wires=wires)
    qml.GlobalPhase(-np.pi / 2, wires=wires)


add_decomps(PauliY, _pauliy_to_ry_gp)


class PauliZ(Observable, Operation):
    r"""
    The Pauli Z operator

    .. math:: \sigma_z = \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix}.

    .. seealso:: The equivalent short-form alias :class:`~Z`

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    resource_keys = set()

    basis = "Z"

    batch_size = None

    resource_keys = set()

    _queue_category = "_ops"

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {qml.pauli.PauliWord({self.wires[0]: "Z"}): 1.0}
            )
        return self._pauli_rep

    def __init__(self, wires: WiresLike, id: Optional[str] = None):
        super().__init__(wires=wires, id=id)

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"Z('{wire}')"
        return f"Z({wire})"

    def label(
        self,
        decimals: Optional[int] = None,
        base_label: Optional[str] = None,
        cache: Optional[dict] = None,
    ) -> str:
        return base_label or "Z"

    @property
    def name(self) -> str:
        return "PauliZ"

    @property
    def resource_params(self) -> dict:
        return {}

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.Z.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.Z.compute_matrix())
        [[ 1  0]
         [ 0 -1]]
        """
        return np.array([[1, 0], [0, -1]])

    @staticmethod
    @lru_cache()
    def compute_sparse_matrix(format="csr") -> sparse.spmatrix:  # pylint: disable=arguments-differ
        return sparse.csr_matrix([[1, 0], [0, -1]]).asformat(format=format)

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.Z.eigvals`

        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.Z.compute_eigvals())
        [ 1 -1]
        """
        return qml.pauli.pauli_eigs(1)

    @staticmethod
    def compute_diagonalizing_gates(  # pylint: disable=unused-argument
        wires: WiresLike,
    ) -> list[qml.operation.Operator]:
        r"""Sequence of gates that diagonalize the operator in the computational basis (static method).

        Given the eigendecomposition :math:`O = U \Sigma U^{\dagger}` where
        :math:`\Sigma` is a diagonal matrix containing the eigenvalues,
        the sequence of diagonalizing gates implements the unitary :math:`U^{\dagger}`.

        The diagonalizing gates rotate the state into the eigenbasis
        of the operator.

        .. seealso:: :meth:`~.Z.diagonalizing_gates`.

        Args:
            wires (Iterable[Any] or Wires): wires that the operator acts on

        Returns:
            list[.Operator]: list of diagonalizing gates

        **Example**

        >>> print(qml.Z.compute_diagonalizing_gates(wires=[0]))
        []
        """
        return []

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.

        .. seealso:: :meth:`~.Z.decomposition`.

        Args:
            wires (Any, Wires): Single wire that the operator acts on.

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.Z.compute_decomposition(0))
        [PhaseShift(3.141592653589793, wires=[0])]

        """
        return [qml.PhaseShift(np.pi, wires=wires)]

    def adjoint(self) -> "PauliZ":
        return Z(wires=self.wires)

    def pow(self, z: float) -> list[qml.operation.Operator]:
        z_mod2 = z % 2
        if z_mod2 == 0:
            return []
        if z_mod2 == 1:
            return [copy(self)]

        if abs(z_mod2 - 0.5) < 1e-6:
            return [S(wires=self.wires)]
        if abs(z_mod2 - 0.25) < 1e-6:
            return [T(wires=self.wires)]

        return [qml.PhaseShift(np.pi * z_mod2, wires=self.wires)]

    def _controlled(self, wire: WiresLike) -> "qml.CZ":
        return qml.CZ(wires=wire + self.wires)

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # Z = RZ(\pi) RY(0) RZ(0)
        return [np.pi, 0.0, 0.0]


Z = PauliZ
r"""The Pauli Z operator

.. math:: \sigma_z = \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix}.

.. seealso:: The equivalent long-form alias :class:`~PauliZ`

**Details:**

* Number of wires: 1
* Number of parameters: 0

Args:
    wires (Sequence[int] or int): the wire the operation acts on
"""


def _pauliz_to_ps_resources():
    return {qml.PhaseShift: 1}


@register_resources(_pauliz_to_ps_resources)
def _pauliz_to_ps(wires: WiresLike, **__):
    qml.PhaseShift(np.pi, wires=wires)


add_decomps(PauliZ, _pauliz_to_ps)


class S(Operation):
    r"""S(wires)
    The single-qubit phase gate

    .. math:: S = \begin{bmatrix}
                1 & 0 \\
                0 & i
            \end{bmatrix}.

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    basis = "Z"

    batch_size = None

    resource_keys = set()

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({self.wires[0]: "I"}): 0.5 + 0.5j,
                    qml.pauli.PauliWord({self.wires[0]: "Z"}): 0.5 - 0.5j,
                }
            )
        return self._pauli_rep

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"S('{wire}')"
        return f"S({wire})"

    @property
    def resource_params(self) -> dict:
        return {}

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.S.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.S.compute_matrix())
        [[1.+0.j 0.+0.j]
         [0.+0.j 0.+1.j]]
        """
        return np.array([[1, 0], [0, 1j]])

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.S.eigvals`

        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.S.compute_eigvals())
        [1.+0.j 0.+1.j]
        """
        return np.array([1, 1j])

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.S.decomposition`.

        Args:
            wires (Any, Wires): Single wire that the operator acts on.

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.S.compute_decomposition(0))
        [PhaseShift(1.5707963267948966, wires=[0])]

        """
        return [qml.PhaseShift(np.pi / 2, wires=wires)]

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        z_mod4 = z % 4
        pow_map = {
            0: lambda op: [],
            0.5: lambda op: [T(wires=op.wires)],
            1: lambda op: [copy(op)],
            2: lambda op: [Z(wires=op.wires)],
        }
        return pow_map.get(z_mod4, lambda op: [qml.PhaseShift(np.pi * z_mod4 / 2, wires=op.wires)])(
            self
        )

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # S = RZ(\pi/2) RY(0) RZ(0)
        return [np.pi / 2, 0.0, 0.0]


def _s_phaseshift_resources():
    return {qml.PhaseShift: 1}


@register_resources(_s_phaseshift_resources)
def _s_phaseshift(wires, **__):
    qml.PhaseShift(np.pi / 2, wires=wires)


add_decomps(S, _s_phaseshift)


class T(Operation):
    r"""T(wires)
    The single-qubit T gate

    .. math:: T = \begin{bmatrix}
                1 & 0 \\
                0 & e^{\frac{i\pi}{4}}
            \end{bmatrix}.

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    basis = "Z"

    batch_size = None

    resource_keys = set()

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({self.wires[0]: "I"}): (0.5 + INV_SQRT2 * (0.5 + 0.5j)),
                    qml.pauli.PauliWord({self.wires[0]: "Z"}): (0.5 - INV_SQRT2 * (0.5 + 0.5j)),
                }
            )
        return self._pauli_rep

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"T('{wire}')"
        return f"T({wire})"

    @property
    def resource_params(self) -> dict:
        return {}

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.T.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.T.compute_matrix())
        [[1.+0.j         0.        +0.j        ]
         [0.+0.j         0.70710678+0.70710678j]]
        """
        return np.array([[1, 0], [0, cmath.exp(1j * np.pi / 4)]])

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.T.eigvals`

        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.T.compute_eigvals())
        [1.+0.j 0.70710678+0.70710678j]
        """
        return np.array([1, cmath.exp(1j * np.pi / 4)])

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.T.decomposition`.

        Args:
            wires (Any, Wires): Single wire that the operator acts on.

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.T.compute_decomposition(0))
        [PhaseShift(0.7853981633974483, wires=[0])]

        """
        return [qml.PhaseShift(np.pi / 4, wires=wires)]

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        z_mod8 = z % 8
        pow_map = {
            0: lambda op: [],
            1: lambda op: [copy(op)],
            2: lambda op: [S(wires=op.wires)],
            4: lambda op: [Z(wires=op.wires)],
        }
        return pow_map.get(z_mod8, lambda op: [qml.PhaseShift(np.pi * z_mod8 / 4, wires=op.wires)])(
            self
        )

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # T = RZ(\pi/4) RY(0) RZ(0)
        return [np.pi / 4, 0.0, 0.0]


def _t_phaseshift_resources():
    return {qml.PhaseShift: 1}


@register_resources(_t_phaseshift_resources)
def _t_phaseshift(wires, **__):
    qml.PhaseShift(np.pi / 4, wires=wires)


add_decomps(T, _t_phaseshift)


class SX(Operation):
    r"""SX(wires)
    The single-qubit Square-Root X operator.

    .. math:: SX = \sqrt{X} = \frac{1}{2} \begin{bmatrix}
            1+i &   1-i \\
            1-i &   1+i \\
        \end{bmatrix}.

    **Details:**

    * Number of wires: 1
    * Number of parameters: 0

    Args:
        wires (Sequence[int] or int): the wire the operation acts on
    """

    num_wires = 1
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    basis = "X"

    resource_keys = set()

    @property
    def resource_params(self) -> dict:
        return {}

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({self.wires[0]: "I"}): (0.5 + 0.5j),
                    qml.pauli.PauliWord({self.wires[0]: "X"}): (0.5 - 0.5j),
                }
            )
        return self._pauli_rep

    def __repr__(self) -> str:
        """String representation."""
        wire = self.wires[0]
        if isinstance(wire, str):
            return f"SX('{wire}')"
        return f"SX({wire})"

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.SX.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.SX.compute_matrix())
        [[0.5+0.5j 0.5-0.5j]
         [0.5-0.5j 0.5+0.5j]]
        """
        return 0.5 * np.array([[1 + 1j, 1 - 1j], [1 - 1j, 1 + 1j]])

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.SX.eigvals`


        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.SX.compute_eigvals())
        [1.+0.j 0.+1.j]
        """
        return np.array([1, 1j])

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.SX.decomposition`.

        Args:
            wires (Any, Wires): Single wire that the operator acts on.

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.SX.compute_decomposition(0))
        [RZ(1.5707963267948966, wires=[0]),
        RY(1.5707963267948966, wires=[0]),
        RZ(-1.5707963267948966, wires=[0]),
        GlobalPhase(-0.7853981633974483, wires=[0])]

        """
        return [
            qml.RZ(np.pi / 2, wires=wires),
            qml.RY(np.pi / 2, wires=wires),
            qml.RZ(-np.pi / 2, wires=wires),
            qml.GlobalPhase(-np.pi / 4, wires=wires),
        ]

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        z_mod4 = z % 4
        if z_mod4 == 2:
            return [X(wires=self.wires)]
        return super().pow(z_mod4)

    def single_qubit_rot_angles(self) -> list[TensorLike]:
        # SX = RZ(-\pi/2) RY(\pi/2) RZ(\pi/2)
        return [np.pi / 2, np.pi / 2, -np.pi / 2]


def _sx_to_rz_ry_rz_ps_resources():
    return {qml.PhaseShift: 1, qml.RZ: 2, qml.RY: 1}


@register_resources(_sx_to_rz_ry_rz_ps_resources)
def _sx_to_rz_ry_rz_ps(wires: WiresLike, **__):
    qml.RZ(np.pi / 2, wires=wires)
    qml.RY(np.pi / 2, wires=wires)
    qml.RZ(-np.pi, wires=wires)
    qml.PhaseShift(np.pi / 2, wires=wires)


add_decomps(SX, _sx_to_rz_ry_rz_ps)


class SWAP(Operation):
    r"""SWAP(wires)
    The swap operator

    .. math:: SWAP = \begin{bmatrix}
            1 & 0 & 0 & 0 \\
            0 & 0 & 1 & 0\\
            0 & 1 & 0 & 0\\
            0 & 0 & 0 & 1
        \end{bmatrix}.

    **Details:**

    * Number of wires: 2
    * Number of parameters: 0

    Args:
        wires (Sequence[int]): the wires the operation acts on
    """

    num_wires = 2
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    resource_keys = set()
    batch_size = None

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({}): 0.5,
                    qml.pauli.PauliWord({self.wires[0]: "X", self.wires[1]: "X"}): 0.5,
                    qml.pauli.PauliWord({self.wires[0]: "Y", self.wires[1]: "Y"}): 0.5,
                    qml.pauli.PauliWord({self.wires[0]: "Z", self.wires[1]: "Z"}): 0.5,
                }
            )
        return self._pauli_rep

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.SWAP.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.SWAP.compute_matrix())
        [[1 0 0 0]
         [0 0 1 0]
         [0 1 0 0]
         [0 0 0 1]]
        """
        return np.array([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]])

    @staticmethod
    @lru_cache()
    def compute_sparse_matrix(format="csr") -> sparse.spmatrix:  # pylint: disable=arguments-differ
        r"""Sparse Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.SWAP.sparse_matrix`

        Returns:
            csr_matrix: matrix

        **Example**

        >>> print(qml.SWAP.compute_sparse_matrix())
        <Compressed Sparse Row sparse matrix of dtype 'int64'
                with 4 stored elements and shape (4, 4)>
          Coords        Values
          (0, 0)        1
          (1, 2)        1
          (2, 1)        1
          (3, 3)        1
        """
        # The same as
        # [[1 0 0 0]
        #  [0 0 1 0]
        #  [0 1 0 0]
        #  [0 0 0 1]]
        data, indices, indptr = [1, 1, 1, 1], [0, 2, 1, 3], [0, 1, 2, 3, 4]
        return sparse.csr_matrix((data, indices, indptr)).asformat(format=format)

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.SWAP.decomposition`.

        Args:
            wires (Iterable, Wires): wires that the operator acts on

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.SWAP.compute_decomposition((0,1)))
        [CNOT(wires=[0, 1]), CNOT(wires=[1, 0]), CNOT(wires=[0, 1])]

        """
        return [
            qml.CNOT(wires=[wires[0], wires[1]]),
            qml.CNOT(wires=[wires[1], wires[0]]),
            qml.CNOT(wires=[wires[0], wires[1]]),
        ]

    @property
    def resource_params(self) -> dict:
        return {}

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        return super().pow(z % 2)

    def adjoint(self) -> "SWAP":
        return SWAP(wires=self.wires)

    def _controlled(self, wire: WiresLike) -> "qml.CSWAP":
        return qml.CSWAP(wires=wire + self.wires)

    @property
    def is_hermitian(self) -> bool:
        return True


def _swap_to_cnot_resources():
    return {qml.CNOT: 3}


@register_resources(_swap_to_cnot_resources)
def _swap_to_cnot(wires, **__):
    qml.CNOT(wires=[wires[0], wires[1]])
    qml.CNOT(wires=[wires[1], wires[0]])
    qml.CNOT(wires=[wires[0], wires[1]])


add_decomps(SWAP, _swap_to_cnot)


class ECR(Operation):
    r""" ECR(wires)

    An echoed RZX(:math:`\pi/2`) gate.

    .. math:: ECR = {\frac{1}{\sqrt{2}}} \begin{bmatrix}
            0 & 0 & 1 & i \\
            0 & 0 & i & 1 \\
            1 & -i & 0 & 0 \\
            -i & 1 & 0 & 0
        \end{bmatrix}.

    **Details:**

    * Number of wires: 2
    * Number of parameters: 0

    Args:
        wires (int): the subsystem the gate acts on
        id (str or None): String representing the operation (optional)
    """

    num_wires = 2
    num_params = 0

    batch_size = None

    resource_keys = set()

    @property
    def resource_params(self) -> dict:
        return {}

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({self.wires[0]: "X"}): INV_SQRT2,
                    qml.pauli.PauliWord({self.wires[0]: "Y", self.wires[1]: "X"}): -INV_SQRT2,
                }
            )
        return self._pauli_rep

    @staticmethod
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.ECR.matrix`


        Return type: tensor_like

        **Example**

        >>> print(qml.ECR.compute_matrix())
         [[0+0.j 0.+0.j 1/sqrt(2)+0.j 0.+1j/sqrt(2)]
         [0.+0.j 0.+0.j 0.+1.j/sqrt(2) 1/sqrt(2)+0.j]
         [1/sqrt(2)+0.j 0.-1.j/sqrt(2) 0.+0.j 0.+0.j]
         [0.-1/sqrt(2)j 1/sqrt(2)+0.j 0.+0.j 0.+0.j]]
        """

        return np.array(
            [
                [0, 0, INV_SQRT2, INV_SQRT2 * 1j],
                [0, 0, INV_SQRT2 * 1j, INV_SQRT2],
                [INV_SQRT2, -INV_SQRT2 * 1j, 0, 0],
                [-INV_SQRT2 * 1j, INV_SQRT2, 0, 0],
            ]
        )

    @staticmethod
    def compute_eigvals() -> np.ndarray:
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.ECR.eigvals`


        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.ECR.compute_eigvals())
        [1, -1, 1, -1]
        """

        return np.array([1, -1, 1, -1])

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

           .. math:: O = O_1 O_2 \dots O_n.


           .. seealso:: :meth:`~.ECR.decomposition`.

           Args:
               wires (Iterable, Wires): wires that the operator acts on

           Returns:
               list[Operator]: decomposition into lower level operations

           **Example:**

           >>> print(qml.ECR.compute_decomposition((0,1)))


        [Z(0),
         CNOT(wires=[0, 1]),
         SX(1),
         RX(1.5707963267948966, wires=[0]),
         RY(1.5707963267948966, wires=[0]),
         RX(1.5707963267948966, wires=[0])]

        """
        pi = np.pi
        return [
            Z(wires=[wires[0]]),
            qml.CNOT(wires=[wires[0], wires[1]]),
            SX(wires=[wires[1]]),
            qml.RX(pi / 2, wires=[wires[0]]),
            qml.RY(pi / 2, wires=[wires[0]]),
            qml.RX(pi / 2, wires=[wires[0]]),
        ]

    def adjoint(self) -> "ECR":
        return ECR(wires=self.wires)

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        return super().pow(z % 2)


def _ecr_decomp_resources():
    return {Z: 1, qml.CNOT: 1, SX: 1, qml.RX: 2, qml.RY: 1}


@register_resources(_ecr_decomp_resources)
def _ecr_decomp(wires, **__):
    Z(wires=[wires[0]])
    qml.CNOT(wires=[wires[0], wires[1]])
    SX(wires=[wires[1]])
    qml.RX(np.pi / 2, wires=[wires[0]])
    qml.RY(np.pi / 2, wires=[wires[0]])
    qml.RX(np.pi / 2, wires=[wires[0]])


add_decomps(ECR, _ecr_decomp)


class ISWAP(Operation):
    r"""ISWAP(wires)
    The i-swap operator

    .. math:: ISWAP = \begin{bmatrix}
            1 & 0 & 0 & 0 \\
            0 & 0 & i & 0\\
            0 & i & 0 & 0\\
            0 & 0 & 0 & 1
        \end{bmatrix}.

    **Details:**

    * Number of wires: 2
    * Number of parameters: 0

    Args:
        wires (Sequence[int]): the wires the operation acts on
    """

    num_wires = 2
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    batch_size = None
    resource_keys = set()

    @property
    def resource_params(self) -> dict:
        return {}

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({}): 0.5,
                    qml.pauli.PauliWord({self.wires[0]: "X", self.wires[1]: "X"}): 0.5j,
                    qml.pauli.PauliWord({self.wires[0]: "Y", self.wires[1]: "Y"}): 0.5j,
                    qml.pauli.PauliWord({self.wires[0]: "Z", self.wires[1]: "Z"}): 0.5,
                }
            )
        return self._pauli_rep

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.ISWAP.matrix`

        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.ISWAP.compute_matrix())
        [[1.+0.j 0.+0.j 0.+0.j 0.+0.j]
         [0.+0.j 0.+0.j 0.+1.j 0.+0.j]
         [0.+0.j 0.+1.j 0.+0.j 0.+0.j]
         [0.+0.j 0.+0.j 0.+0.j 1.+0.j]]
        """
        return np.array([[1, 0, 0, 0], [0, 0, 1j, 0], [0, 1j, 0, 0], [0, 0, 0, 1]])

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.ISWAP.eigvals`


        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.ISWAP.compute_eigvals())
        [1j, -1j, 1, 1]
        """
        return np.array([1j, -1j, 1, 1])

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.ISWAP.decomposition`.

        Args:
            wires (Iterable, Wires): wires that the operator acts on

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.ISWAP.compute_decomposition((0,1)))
        [S(0),
        S(1),
        H(0),
        CNOT(wires=[0, 1]),
        CNOT(wires=[1, 0]),
        H(1)]

        """
        return [
            S(wires=wires[0]),
            S(wires=wires[1]),
            Hadamard(wires=wires[0]),
            qml.CNOT(wires=[wires[0], wires[1]]),
            qml.CNOT(wires=[wires[1], wires[0]]),
            Hadamard(wires=wires[1]),
        ]

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        z_mod2 = z % 2
        if abs(z_mod2 - 0.5) < 1e-6:
            return [SISWAP(wires=self.wires)]
        return super().pow(z_mod2)


def _iswap_decomp_resources():
    return {qml.S: 2, qml.Hadamard: 2, qml.CNOT: 2}


@register_resources(_iswap_decomp_resources)
def _iswap_decomp(wires, **__):
    S(wires=wires[0])
    S(wires=wires[1])
    Hadamard(wires=wires[0])
    qml.CNOT(wires=[wires[0], wires[1]])
    qml.CNOT(wires=[wires[1], wires[0]])
    Hadamard(wires=wires[1])


add_decomps(ISWAP, _iswap_decomp)


class SISWAP(Operation):
    r"""SISWAP(wires)
    The square root of i-swap operator. Can also be accessed as ``qml.SQISW``

    .. math:: SISWAP = \begin{bmatrix}
            1 & 0 & 0 & 0 \\
            0 & 1/ \sqrt{2} & i/\sqrt{2} & 0\\
            0 & i/ \sqrt{2} & 1/ \sqrt{2} & 0\\
            0 & 0 & 0 & 1
        \end{bmatrix}.

    **Details:**

    * Number of wires: 2
    * Number of parameters: 0

    Args:
        wires (Sequence[int]): the wires the operation acts on
    """

    num_wires = 2
    num_params = 0
    """int: Number of trainable parameters that the operator depends on."""

    batch_size = None
    resource_keys = set()

    @property
    def resource_params(self) -> dict:
        return {}

    @property
    def pauli_rep(self):
        if self._pauli_rep is None:
            self._pauli_rep = qml.pauli.PauliSentence(
                {
                    qml.pauli.PauliWord({self.wires[0]: "I", self.wires[1]: "I"}): 0.5
                    + 0.5 * INV_SQRT2,
                    qml.pauli.PauliWord({self.wires[0]: "X", self.wires[1]: "X"}): 0.5j * INV_SQRT2,
                    qml.pauli.PauliWord({self.wires[0]: "Y", self.wires[1]: "Y"}): 0.5j * INV_SQRT2,
                    qml.pauli.PauliWord({self.wires[0]: "Z", self.wires[1]: "Z"}): 0.5
                    - 0.5 * INV_SQRT2,
                }
            )
        return self._pauli_rep

    @staticmethod
    @lru_cache()
    def compute_matrix() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Representation of the operator as a canonical matrix in the computational basis (static method).

        The canonical matrix is the textbook matrix representation that does not consider wires.
        Implicitly, this assumes that the wires of the operator correspond to the global wire order.

        .. seealso:: :meth:`~.SISWAP.matrix`


        Returns:
            ndarray: matrix

        **Example**

        >>> print(qml.SISWAP.compute_matrix())
        [[1.+0.j          0.+0.j          0.+0.j  0.+0.j]
         [0.+0.j  0.70710678+0.j  0.+0.70710678j  0.+0.j]
         [0.+0.j  0.+0.70710678j  0.70710678+0.j  0.+0.j]
         [0.+0.j          0.+0.j          0.+0.j  1.+0.j]]
        """
        return np.array(
            [
                [1, 0, 0, 0],
                [0, INV_SQRT2, INV_SQRT2 * 1j, 0],
                [0, INV_SQRT2 * 1j, INV_SQRT2, 0],
                [0, 0, 0, 1],
            ]
        )

    @staticmethod
    def compute_eigvals() -> np.ndarray:  # pylint: disable=arguments-differ
        r"""Eigenvalues of the operator in the computational basis (static method).

        If :attr:`diagonalizing_gates` are specified and implement a unitary :math:`U^{\dagger}`,
        the operator can be reconstructed as

        .. math:: O = U \Sigma U^{\dagger},

        where :math:`\Sigma` is the diagonal matrix containing the eigenvalues.

        Otherwise, no particular order for the eigenvalues is guaranteed.

        .. seealso:: :meth:`~.SISWAP.eigvals`


        Returns:
            array: eigenvalues

        **Example**

        >>> print(qml.SISWAP.compute_eigvals())
        [0.70710678+0.70710678j 0.70710678-0.70710678j 1.+0.j 1.+0.j]
        """
        return np.array([INV_SQRT2 * (1 + 1j), INV_SQRT2 * (1 - 1j), 1, 1])

    @staticmethod
    def compute_decomposition(wires: WiresLike) -> list[qml.operation.Operator]:
        r"""Representation of the operator as a product of other operators (static method).

        .. math:: O = O_1 O_2 \dots O_n.


        .. seealso:: :meth:`~.SISWAP.decomposition`.

        Args:
            wires (Iterable, Wires): wires that the operator acts on

        Returns:
            list[Operator]: decomposition into lower level operations

        **Example:**

        >>> print(qml.SISWAP.compute_decomposition((0,1)))
        [SX(0)),
        RZ(1.5707963267948966, wires=[0]),
        CNOT(wires=[0, 1]),
        SX(0),
        RZ(5.497787143782138, wires=[0]),
        SX(0),
        RZ(1.5707963267948966, wires=[0]),
        SX(1),
        RZ(5.497787143782138, wires=[1]),
        CNOT(wires=[0, 1]),
        SX(0),
        SX(1)]

        """
        return [
            SX(wires=wires[0]),
            qml.RZ(np.pi / 2, wires=wires[0]),
            qml.CNOT(wires=[wires[0], wires[1]]),
            SX(wires=wires[0]),
            qml.RZ(7 * np.pi / 4, wires=wires[0]),
            SX(wires=wires[0]),
            qml.RZ(np.pi / 2, wires=wires[0]),
            SX(wires=wires[1]),
            qml.RZ(7 * np.pi / 4, wires=wires[1]),
            qml.CNOT(wires=[wires[0], wires[1]]),
            SX(wires=wires[0]),
            SX(wires=wires[1]),
        ]

    def pow(self, z: Union[int, float]) -> list[qml.operation.Operator]:
        z_mod4 = z % 4
        return [ISWAP(wires=self.wires)] if z_mod4 == 2 else super().pow(z_mod4)


def _siswap_decomp_resources():
    return {SX: 6, qml.RZ: 4, qml.CNOT: 2}


@register_resources(_siswap_decomp_resources)
def _siswap_decomp(wires, **__):
    SX(wires=wires[0])
    qml.RZ(np.pi / 2, wires=wires[0])
    qml.CNOT(wires=[wires[0], wires[1]])
    SX(wires=wires[0])
    qml.RZ(7 * np.pi / 4, wires=wires[0])
    SX(wires=wires[0])
    qml.RZ(np.pi / 2, wires=wires[0])
    SX(wires=wires[1])
    qml.RZ(7 * np.pi / 4, wires=wires[1])
    qml.CNOT(wires=[wires[0], wires[1]])
    SX(wires=wires[0])
    SX(wires=wires[1])


add_decomps(SISWAP, _siswap_decomp)

SQISW = SISWAP

_modules/pennylane/ops/qubit/non_parametric_ops

 

Download Python script

 

Download Notebook

 

View on GitHub