Source code for pennylane.fourier.utils

# 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.
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"""Contains utility functions for the Fourier module."""

from itertools import product, combinations
import numpy as np


import pennylane as qml


def format_nvec(nvec):
    """Nice strings representing tuples of integers."""

    if isinstance(nvec, int):
        return str(nvec)

    nvec_str = [f"{n}" if n < 0 else f" {n}" for n in nvec]

    return " ".join(nvec_str)


def to_dict(coeffs):
    """Convert a set of indices to a dictionary."""
    # infer hyperparameters
    degree = coeffs.shape[0] // 2
    n_inputs = len(coeffs.shape)

    # create generator for indices nvec = (n1, ..., nN),
    # ranging from (-d,...,-d) to (d,...,d).
    n_range = np.array(range(-degree, degree + 1))
    n_ranges = [n_range] * n_inputs
    nvecs = product(*n_ranges)

    return {nvec: coeffs[nvec] for nvec in nvecs}


[docs]def get_spectrum(op, decimals): r"""Extract the frequencies contributed by an input-encoding gate to the overall Fourier representation of a quantum circuit. If :math:`G` is the generator of the input-encoding gate :math:`\exp(-i x G)`, the frequencies are the differences between any two of :math:`G`'s eigenvalues. We only compute non-negative frequencies in this subroutine. Args: op (~pennylane.operation.Operation): Operation to extract the frequencies for decimals (int): Number of decimal places to round the frequencies to Returns: set[float]: non-negative frequencies contributed by this input-encoding gate """ matrix = qml.matrix(qml.generator(op, format="observable")) # todo: use qml.math.linalg once it is tested properly evals = np.linalg.eigvalsh(matrix) # compute all unique positive differences of eigenvalues, then add 0 # note that evals are sorted already _spectrum = set(np.round([x[1] - x[0] for x in combinations(evals, 2)], decimals=decimals)) _spectrum |= {0} return _spectrum
[docs]def join_spectra(spec1, spec2): r"""Join two sets of frequencies that belong to the same input. Since :math:`\exp(i a x)\exp(i b x) = \exp(i (a+b) x)`, the spectra of two gates encoding the same :math:`x` are joined by computing the set of sums and absolute values of differences of their elements. We only compute non-negative frequencies in this subroutine and assume the inputs to be non-negative frequencies as well. Args: spec1 (set[float]): first spectrum spec2 (set[float]): second spectrum Returns: set[float]: joined spectrum """ if spec1 == {0}: return spec2 if spec2 == {0}: return spec1 sums = set() diffs = set() for s1 in spec1: for s2 in spec2: sums.add(s1 + s2) diffs.add(np.abs(s1 - s2)) return sums.union(diffs)