Source code for pennylane.templates.state_preparations.cosine_window

# 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.
r"""
Contains the CosineWindow template.
"""
import numpy as np

import pennylane as qml
from pennylane import math
from pennylane.operation import StatePrepBase
from pennylane.wires import WireError, Wires


class CosineWindow(StatePrepBase):
    r"""CosineWindow(wires)
    Prepares an initial state with a cosine wave function.

    The wave function is defined below where :math:`m` is the number of wires.

    .. math::

        |\psi\rangle = \sqrt{2^{1-m}} \sum_{k=0}^{2^m-1} \cos(\frac{\pi k}{2^m} - \frac{\pi}{2}) |k\rangle,

    .. figure:: ../../_static/templates/state_preparations/cosine_window.png
        :align: center
        :width: 65%
        :target: javascript:void(0);

    .. note::

        The wave function is shifted by :math:`\frac{\pi}{2}` units so that the window is centered.

    For more details see `Phys. Rev. D 106 (2022) <https://journals.aps.org/prd/abstract/10.1103/PhysRevD.106.034503>`_.

    .. seealso:: :class:`~.QuantumPhaseEstimation` and :class:`~.QFT`.

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

    **Example**

    >>> dev = qml.device('default.qubit', wires=2)
    >>> @qml.qnode(dev)
    ... def example_circuit():
    ...     qml.CosineWindow(wires=range(2))
    ...     return qml.probs()
    >>> print(example_circuit())
    [1.87469973e-33 2.50000000e-01 5.00000000e-01 2.50000000e-01]
    """

    @staticmethod
    def compute_decomposition(wires):  # pylint: disable=arguments-differ,unused-argument
        r"""Representation of the operator as a product of other operators (static method).
        It is efficiently decomposed from one QFT over all qubits and one-qubit rotation gates.

        Args:
            wires (Iterable, Wires): the wire(s) the operation acts on

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

        decomp_ops = []

        decomp_ops.append(qml.Hadamard(wires=wires[-1]))
        decomp_ops.append(qml.RZ(np.pi, wires=wires[-1]))
        decomp_ops.append(qml.adjoint(qml.QFT)(wires=wires))

        for ind, wire in enumerate(wires):
            decomp_ops.append(qml.PhaseShift(np.pi * 2 ** (-ind - 1), wires=wire))

        return decomp_ops

    def label(self, decimals=None, base_label=None, cache=None):
        return "CosineWindow"

    def state_vector(self, wire_order=None):  # pylint: disable=arguments-differ,unused-argument
        r"""Calculation of the state vector generated by the cosine window.

        Args:
            wire_order (Iterable, Wires): Custom order of wires for the returned state vector.

        Raises:
            WireError: Custom wire_order must contain all wires.

        Returns:
            TensorLike[complex]: output state
        """

        num_op_wires = len(self.wires)
        op_vector_shape = (2,) * num_op_wires
        coeff = np.sqrt(2 ** (1 - num_op_wires))
        vector = np.array(
            [
                coeff * np.cos(-np.pi / 2 + np.pi * x / 2**num_op_wires)
                for x in range(2**num_op_wires)
            ]
        )
        op_vector = math.reshape(vector, op_vector_shape)

        if wire_order is None or Wires(wire_order) == self.wires:
            return op_vector

        wire_order = Wires(wire_order)
        if not wire_order.contains_wires(self.wires):
            raise WireError(f"Custom wire_order must contain all {self.name} wires")

        num_total_wires = len(wire_order)
        indices = tuple(
            [Ellipsis] + [slice(None)] * num_op_wires + [0] * (num_total_wires - num_op_wires)
        )
        ket_shape = [2] * num_total_wires
        ket = np.zeros(ket_shape, dtype=np.complex128)
        ket[indices] = op_vector

        if self.wires != wire_order[:num_op_wires]:
            current_order = self.wires + list(Wires.unique_wires([wire_order, self.wires]))
            desired_order = [current_order.index(w) for w in wire_order]
            ket = ket.transpose(desired_order)

        return math.convert_like(ket, op_vector)

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