Source code for pennylane.ops.qubit.state_preparation

# 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 concerned
with preparing a certain state on the device.
"""
# pylint:disable=abstract-method,arguments-differ,protected-access,no-member
from pennylane import numpy as np
from pennylane import math
from pennylane.operation import AnyWires, Operation, StatePrep
from pennylane.templates.state_preparations import BasisStatePreparation, MottonenStatePreparation
from pennylane.wires import Wires, WireError

state_prep_ops = {"BasisState", "QubitStateVector", "QubitDensityMatrix"}


class BasisState(StatePrep):
    r"""BasisState(n, wires)
    Prepares a single computational basis state.

    **Details:**

    * Number of wires: Any (the operation can act on any number of wires)
    * Number of parameters: 1
    * Gradient recipe: None (integer parameters not supported)

    .. note::

        If the ``BasisState`` operation is not supported natively on the
        target device, PennyLane will attempt to decompose the operation
        into :class:`~.PauliX` operations.

    Args:
        n (array): prepares the basis state :math:`\ket{n}`, where ``n`` is an
            array of integers from the set :math:`\{0, 1\}`, i.e.,
            if ``n = np.array([0, 1, 0])``, prepares the state :math:`|010\rangle`.
        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.BasisState(np.array([1, 1]), wires=range(2))
    ...     return qml.state()
    >>> print(example_circuit())
    [0.+0.j 0.+0.j 0.+0.j 1.+0.j]
    """
    num_wires = AnyWires
    num_params = 1
    """int: Number of trainable parameters that the operator depends on."""

    @staticmethod
    def compute_decomposition(n, wires):
        r"""Representation of the operator as a product of other operators (static method). :

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


        .. seealso:: :meth:`~.BasisState.decomposition`.

        Args:
            n (array): prepares the basis state :math:`\ket{n}`, where ``n`` is an
                array of integers from the set :math:`\{0, 1\}`
            wires (Iterable, Wires): the wire(s) the operation acts on

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

        **Example:**

        >>> qml.BasisState.compute_decomposition([1,0], wires=(0,1))
        [BasisStatePreparation([1, 0], wires=[0, 1])]

        """
        return [BasisStatePreparation(n, wires)]

    def state_vector(self, wire_order=None):
        """Returns a state-vector of shape ``(2,) * num_wires``."""
        prep_vals = self.parameters[0]
        if any(i not in [0, 1] for i in prep_vals):
            raise ValueError("BasisState parameter must consist of 0 or 1 integers.")

        if (num_wires := len(self.wires)) != len(prep_vals):
            raise ValueError("BasisState parameter and wires must be of equal length.")

        if wire_order is None:
            indices = prep_vals
        else:
            if not Wires(wire_order).contains_wires(self.wires):
                raise WireError("Custom wire_order must contain all BasisState wires")
            num_wires = len(wire_order)
            indices = [0] * num_wires
            for base_wire_label, value in zip(self.wires, prep_vals):
                indices[wire_order.index(base_wire_label)] = value

        ket = np.zeros((2,) * num_wires)
        ket[tuple(indices)] = 1
        return math.convert_like(ket, prep_vals)


class QubitStateVector(StatePrep):
    r"""QubitStateVector(state, wires)
    Prepare subsystems using the given ket vector in the computational basis.

    **Details:**

    * Number of wires: Any (the operation can act on any number of wires)
    * Number of parameters: 1
    * Gradient recipe: None

    .. note::

        If the ``QubitStateVector`` operation is not supported natively on the
        target device, PennyLane will attempt to decompose the operation
        using the method developed by Möttönen et al. (Quantum Info. Comput.,
        2005).

    Args:
        state (array[complex]): a state vector of size 2**len(wires)
        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.QubitStateVector(np.array([1, 0, 0, 0]), wires=range(2))
    ...     return qml.state()
    >>> print(example_circuit())
    [1.+0.j 0.+0.j 0.+0.j 0.+0.j]
    """
    num_wires = AnyWires
    num_params = 1
    """int: Number of trainable parameters that the operator depends on."""

    ndim_params = (1,)
    """int: Number of dimensions per trainable parameter of the operator."""

    def __init__(self, state, wires, do_queue=True, id=None):
        super().__init__(state, wires=wires, do_queue=do_queue, id=id)
        state = self.parameters[0]

        if len(state.shape) == 1:
            state = math.reshape(state, (1, state.shape[0]))
        if state.shape[1] != 2 ** len(self.wires):
            raise ValueError("State vector must have shape (2**wires,) or (batch_size, 2**wires).")

        param = math.cast(state, np.complex128)
        if not math.is_abstract(param):
            norm = math.linalg.norm(param, axis=-1, ord=2)
            if not math.allclose(norm, 1.0, atol=1e-10):
                raise ValueError("Sum of amplitudes-squared does not equal one.")

    @staticmethod
    def compute_decomposition(state, wires):
        r"""Representation of the operator as a product of other operators (static method). :

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


        .. seealso:: :meth:`~.QubitStateVector.decomposition`.

        Args:
            state (array[complex]): a state vector of size 2**len(wires)
            wires (Iterable, Wires): the wire(s) the operation acts on

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

        **Example:**

        >>> qml.QubitStateVector.compute_decomposition(np.array([1, 0, 0, 0]), wires=range(2))
        [MottonenStatePreparation(tensor([1, 0, 0, 0], requires_grad=True), wires=[0, 1])]

        """
        return [MottonenStatePreparation(state, wires)]

    def state_vector(self, wire_order=None):
        num_op_wires = len(self.wires)
        op_vector = math.reshape(self.parameters[0], (2,) * num_op_wires)

        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("Custom wire_order must contain all QubitStateVector wires")

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

        # unless wire_order is [*self.wires, *rest_of_wire_order], need to rearrange
        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)


class QubitDensityMatrix(Operation):
    r"""QubitDensityMatrix(state, wires)
    Prepare subsystems using the given density matrix.
    If not all the wires are specified, remaining dimension is filled by :math:`\mathrm{tr}_{in}(\rho)`,
    where :math:`\rho` is the full system density matrix before this operation and :math:`\mathrm{tr}_{in}` is a
    partial trace over the subsystem to be replaced by input state.

    **Details:**

    * Number of wires: Any (the operation can act on any number of wires)
    * Number of parameters: 1
    * Gradient recipe: None

    .. note::

        Exception raised if the ``QubitDensityMatrix`` operation is not supported natively on the
        target device.

    Args:
        state (array[complex]): a density matrix of size ``(2**len(wires), 2**len(wires))``
        wires (Sequence[int] or int): the wire(s) the operation acts on

    .. details::
        :title: Usage Details

        Example:

        .. code-block:: python

            import pennylane as qml
            nr_wires = 2
            rho = np.zeros((2 ** nr_wires, 2 ** nr_wires), dtype=np.complex128)
            rho[0, 0] = 1  # initialize the pure state density matrix for the |0><0| state

            dev = qml.device("default.mixed", wires=2)
            @qml.qnode(dev)
            def circuit():
                qml.QubitDensityMatrix(rho, wires=[0, 1])
                return qml.state()

        Running this circuit:

        >>> circuit()
        [[1.+0.j 0.+0.j 0.+0.j 0.+0.j]
         [0.+0.j 0.+0.j 0.+0.j 0.+0.j]
         [0.+0.j 0.+0.j 0.+0.j 0.+0.j]
         [0.+0.j 0.+0.j 0.+0.j 0.+0.j]]
    """
    num_wires = AnyWires
    num_params = 1
    """int: Number of trainable parameters that the operator depends on."""

    grad_method = None

    # This is a temporary attribute to fix the operator queuing behaviour
    _queue_category = "_prep"

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