Source code for pennylane.templates.embeddings.iqp

# Copyright 2018-2021 Xanadu Quantum Technologies Inc.

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r"""
Contains the IQPEmbedding template.
"""
# pylint: disable-msg=too-many-branches,too-many-arguments,protected-access
from itertools import combinations

import pennylane as qml
from pennylane.operation import Operation, AnyWires


[docs]class IQPEmbedding(Operation): r""" Encodes :math:`n` features into :math:`n` qubits using diagonal gates of an IQP circuit. The embedding has been proposed by `Havlicek et al. (2018) <https://arxiv.org/pdf/1804.11326.pdf>`_. The basic IQP circuit can be repeated by specifying ``n_repeats``. Repetitions can make the embedding "richer" through interference. .. warning:: ``IQPEmbedding`` calls a circuit that involves non-trivial classical processing of the features. The ``features`` argument is therefore **not differentiable** when using the template, and gradients with respect to the features cannot be computed by PennyLane. An IQP circuit is a quantum circuit of a block of Hadamards, followed by a block of gates that are diagonal in the computational basis. Here, the diagonal gates are single-qubit ``RZ`` rotations, applied to each qubit and encoding the :math:`n` features, followed by two-qubit ZZ entanglers, :math:`e^{-i x_i x_j \sigma_z \otimes \sigma_z}`. The entangler applied to wires ``(wires[i], wires[j])`` encodes the product of features ``features[i]*features[j]``. The pattern in which the entanglers are applied is either the default, or a custom pattern: * If ``pattern`` is not specified, the default pattern will be used, in which the entangling gates connect all pairs of neighbours: | .. figure:: ../../_static/templates/embeddings/iqp.png :align: center :width: 50% :target: javascript:void(0); | * Else, ``pattern`` is a list of wire pairs ``[[a, b], [c, d],...]``, applying the entangler on wires ``[a, b]``, ``[c, d]``, etc. For example, ``pattern = [[0, 1], [1, 2]]`` produces the following entangler pattern: | .. figure:: ../../_static/templates/embeddings/iqp_custom.png :align: center :width: 50% :target: javascript:void(0); | Since diagonal gates commute, the order of the entanglers does not change the result. Args: features (tensor_like): tensor of features to encode wires (Iterable): wires that the template acts on n_repeats (int): number of times the basic embedding is repeated pattern (list[int]): specifies the wires and features of the entanglers Raises: ValueError: if inputs do not have the correct format .. UsageDetails:: A typical usage example of the template is the following: .. code-block:: python import pennylane as qml from pennylane.templates import IQPEmbedding dev = qml.device('default.qubit', wires=3) @qml.qnode(dev) def circuit(features): IQPEmbedding(features, wires=range(3)) return [qml.expval(qml.PauliZ(w)) for w in range(3)] circuit([1., 2., 3.]) **Repeating the embedding** The embedding can be repeated by specifying the ``n_repeats`` argument: .. code-block:: python @qml.qnode(dev) def circuit(features): IQPEmbedding(features, wires=range(3), n_repeats=4) return [qml.expval(qml.PauliZ(w)) for w in range(3)] circuit([1., 2., 3.]) Every repetition uses exactly the same quantum circuit. **Using a custom entangler pattern** A custom entangler pattern can be used by specifying the ``pattern`` argument. A pattern has to be a nested list of dimension ``(K, 2)``, where ``K`` is the number of entanglers to apply. .. code-block:: python pattern = [[1, 2], [0, 2], [1, 0]] @qml.qnode(dev) def circuit(features): IQPEmbedding(features, wires=range(3), pattern=pattern) return [qml.expval(qml.PauliZ(w)) for w in range(3)] circuit([1., 2., 3.]) Since diagonal gates commute, the order of the wire pairs has no effect on the result. .. code-block:: python from pennylane import numpy as np pattern1 = [[1, 2], [0, 2], [1, 0]] pattern2 = [[1, 0], [0, 2], [1, 2]] # a reshuffling of pattern1 @qml.qnode(dev) def circuit(features, pattern): IQPEmbedding(features, wires=range(3), pattern=pattern, n_repeats=3) return [qml.expval(qml.PauliZ(w)) for w in range(3)] res1 = circuit([1., 2., 3.], pattern=pattern1) res2 = circuit([1., 2., 3.], pattern=pattern2) assert np.allclose(res1, res2) **Non-consecutive wires** In principle, the user can also pass a non-consecutive wire list to the template. For single qubit gates, the i'th feature is applied to the i'th wire index (which may not be the i'th wire). For the entanglers, the product of i'th and j'th features is applied to the wire indices at the i'th and j'th position in ``wires``. For example, for ``wires=[2, 0, 1]`` the ``RZ`` block applies the first feature to wire 2, the second feature to wire 0, and the third feature to wire 1. Likewise, using the default pattern, the entangler block applies the product of the first and second feature to the wire pair ``[2, 0]``, the product of the second and third feature to ``[2, 1]``, and so forth. """ num_params = 1 num_wires = AnyWires par_domain = "A" def __init__(self, features, wires, n_repeats=1, pattern=None, do_queue=True, id=None): shape = qml.math.shape(features) if len(shape) != 1: raise ValueError(f"Features must be a one-dimensional tensor; got shape {shape}.") n_features = shape[0] if n_features != len(wires): raise ValueError(f"Features must be of length {len(wires)}; got length {n_features}.") if pattern is None: # default is an all-to-all pattern pattern = combinations(wires, 2) self.pattern = pattern self.n_repeats = n_repeats super().__init__(features, wires=wires, do_queue=do_queue, id=id)
[docs] def expand(self): features = self.parameters[0] with qml.tape.QuantumTape() as tape: for _ in range(self.n_repeats): for i in range(len(self.wires)): qml.Hadamard(wires=self.wires[i]) qml.RZ(features[i], wires=self.wires[i]) for wire_pair in self.pattern: # get the position of the wire indices in the array idx1, idx2 = self.wires.indices(wire_pair) # apply product of two features as entangler qml.MultiRZ(features[idx1] * features[idx2], wires=wire_pair) return tape