Source code for pennylane.templates.state_preparations.arbitrary_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.
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#     http://www.apache.org/licenses/LICENSE-2.0

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r"""
Contains the ArbitraryStatePreparation template.
"""
# pylint: disable=trailing-comma-tuple
import functools
import pennylane as qml
from pennylane.operation import Operation, AnyWires


@functools.lru_cache()
def _state_preparation_pauli_words(num_wires):
    """Pauli words necessary for a state preparation.

    Args:
        num_wires (int): Number of wires of the state preparation

    Returns:
        List[str]: List of all necessary Pauli words for the state preparation
    """
    if num_wires == 1:
        return ["X", "Y"]

    sub_pauli_words = _state_preparation_pauli_words(num_wires - 1)
    sub_id = "I" * (num_wires - 1)

    single_qubit_words = ["X" + sub_id, "Y" + sub_id]
    multi_qubit_words = list(map(lambda word: "I" + word, sub_pauli_words)) + list(
        map(lambda word: "X" + word, sub_pauli_words)
    )

    return single_qubit_words + multi_qubit_words


[docs]class ArbitraryStatePreparation(Operation): """Implements an arbitrary state preparation on the specified wires. An arbitrary state on :math:`n` wires is parametrized by :math:`2^{n+1} - 2` independent real parameters. This templates uses Pauli word rotations to parametrize the unitary. Args: weights (tensor_like): Angles of the Pauli word rotations. Needs to have length :math:`2^{n+1} - 2` where :math:`n` is the number of wires the template acts upon. wires (Iterable): wires that the template acts on **Example** ArbitraryStatePreparation can be used to train state preparations, for example using a circuit with some measurement observable ``H``: .. code-block:: python dev = qml.device("default.qubit", wires=4) @qml.qnode(dev) def vqe(weights): qml.ArbitraryStatePreparation(weights, wires=[0, 1, 2, 3]) return qml.expval(qml.Hermitian(H, wires=[0, 1, 2, 3])) The shape of the weights parameter can be computed as follows: .. code-block:: python shape = qml.ArbitraryStatePreparation.shape(n_wires=4) """ num_wires = AnyWires grad_method = None def __init__(self, weights, wires, do_queue=True, id=None): shape = qml.math.shape(weights) if shape != (2 ** (len(wires) + 1) - 2,): raise ValueError( f"Weights tensor must be of shape {(2 ** (len(wires) + 1) - 2,)}; got {shape}." ) super().__init__(weights, wires=wires, do_queue=do_queue, id=id) @property def num_params(self): return 1
[docs] @staticmethod def compute_decomposition(weights, wires): # pylint: disable=arguments-differ r"""Representation of the operator as a product of other operators. .. math:: O = O_1 O_2 \dots O_n. .. seealso:: :meth:`~.ArbitraryStatePreparation.decomposition`. Args: weights (tensor_like): Angles of the Pauli word rotations. Needs to have length :math:`2^{n+1} - 2` where :math:`n` is the number of wires the template acts upon. wires (Any or Iterable[Any]): wires that the operator acts on Returns: list[.Operator]: decomposition of the operator **Example** >>> weights = torch.tensor([1., 2., 3., 4., 5., 6.]) >>> qml.ArbitraryStatePreparation.compute_decomposition(weights, wires=["a", "b"]) [PauliRot(tensor(1.), 'XI', wires=['a', 'b']), PauliRot(tensor(2.), 'YI', wires=['a', 'b']), PauliRot(tensor(3.), 'IX', wires=['a', 'b']), PauliRot(tensor(4.), 'IY', wires=['a', 'b']), PauliRot(tensor(5.), 'XX', wires=['a', 'b']), PauliRot(tensor(6.), 'XY', wires=['a', 'b'])] """ op_list = [] for i, pauli_word in enumerate(_state_preparation_pauli_words(len(wires))): op_list.append(qml.PauliRot(weights[i], pauli_word, wires=wires)) return op_list
[docs] @staticmethod def shape(n_wires): r"""Returns the required shape for the weight tensor. Args: n_wires (int): number of wires Returns: tuple[int]: shape """ return (2 ** (n_wires + 1) - 2,)