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

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"""
This file contains functionalities that simplify working with kernels.
"""
from pennylane import numpy as np


[docs]def square_kernel_matrix(X, kernel, assume_normalized_kernel=False): r"""Computes the square matrix of pairwise kernel values for a given dataset. Args: X (list[datapoint]): List of datapoints kernel ((datapoint, datapoint) -> float): Kernel function that maps datapoints to kernel value. assume_normalized_kernel (bool, optional): Assume that the kernel is normalized, in which case the diagonal of the kernel matrix is set to 1, avoiding unnecessary computations. Returns: array[float]: The square matrix of kernel values. **Example:** Consider a simple kernel function based on :class:`~.templates.embeddings.AngleEmbedding`: .. code-block :: python dev = qml.device('default.qubit', wires=2, shots=None) @qml.qnode(dev) def circuit(x1, x2): qml.templates.AngleEmbedding(x1, wires=dev.wires) qml.adjoint(qml.templates.AngleEmbedding)(x2, wires=dev.wires) return qml.probs(wires=dev.wires) kernel = lambda x1, x2: circuit(x1, x2)[0] We can then compute the kernel matrix on a set of 4 (random) feature vectors ``X`` via >>> X = np.random.random((4, 2)) >>> qml.kernels.square_kernel_matrix(X, kernel) tensor([[1. , 0.9532702 , 0.96864001, 0.90932897], [0.9532702 , 1. , 0.99727485, 0.95685561], [0.96864001, 0.99727485, 1. , 0.96605621], [0.90932897, 0.95685561, 0.96605621, 1. ]], requires_grad=True) """ N = len(X) matrix = [0] * N ** 2 for i in range(N): for j in range(i, N): if assume_normalized_kernel and i == j: matrix[N * i + j] = 1.0 else: matrix[N * i + j] = kernel(X[i], X[j]) matrix[N * j + i] = matrix[N * i + j] return np.array(matrix).reshape((N, N))
[docs]def kernel_matrix(X1, X2, kernel): r"""Computes the matrix of pairwise kernel values for two given datasets. Args: X1 (list[datapoint]): List of datapoints (first argument) X2 (list[datapoint]): List of datapoints (second argument) kernel ((datapoint, datapoint) -> float): Kernel function that maps datapoints to kernel value. Returns: array[float]: The square matrix of kernel values. **Example:** Consider a simple kernel function based on :class:`~.templates.embeddings.AngleEmbedding`: .. code-block :: python dev = qml.device('default.qubit', wires=2, shots=None) @qml.qnode(dev) def circuit(x1, x2): qml.templates.AngleEmbedding(x1, wires=dev.wires) qml.adjoint(qml.templates.AngleEmbedding)(x2, wires=dev.wires) return qml.probs(wires=dev.wires) kernel = lambda x1, x2: circuit(x1, x2)[0] With this method we can systematically evaluate the kernel function ``kernel`` on pairs of datapoints, where the points stem from different datasets, like a training and a test dataset. >>> X_train = np.random.random((4,2)) >>> X_test = np.random.random((3,2)) >>> qml.kernels.kernel_matrix(X_train, X_test, kernel) tensor([[0.88875298, 0.90655175, 0.89926447], [0.93762197, 0.98163781, 0.93076383], [0.91977339, 0.9799841 , 0.91582698], [0.80376818, 0.98720925, 0.79349212]], requires_grad=True) As we can see, for :math:`n` and :math:`m` datapoints in the first and second dataset respectively, the output matrix has the shape :math:`n\times m`. """ N = len(X1) M = len(X2) matrix = [0] * N * M for i in range(N): for j in range(M): matrix[M * i + j] = kernel(X1[i], X2[j]) return np.array(matrix).reshape((N, M))