Classical Artificial Neural Network Training Using Quantum Walks as a Search Procedure

Abstract

This article proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic weights of a classical artificial neural network. Each vertex of this complete graph represents a possible synaptic weight set in the <inline-formula><tex-math notation="LaTeX">$w$</tex-math><alternatives><mml:math><mml:mi>w</mml:mi></mml:math><inline-graphic xlink:href="desouza-ieq1-3051559.gif"/></alternatives></inline-formula>-dimensional search space, where <inline-formula><tex-math notation="LaTeX">$w$</tex-math><alternatives><mml:math><mml:mi>w</mml:mi></mml:math><inline-graphic xlink:href="desouza-ieq2-3051559.gif"/></alternatives></inline-formula> is the number of weights of the neural network. To know the number of iterations required <italic>a priori</italic> to obtain the solutions is one of the main advantages of the procedure. Another advantage is that the proposed method does not stagnate in local minimums. Thus, it is possible to use the quantum walk search procedure as an alternative to the backpropagation algorithm. The proposed method was employed for a <inline-formula><tex-math notation="LaTeX">$XOR$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>X</mml:mi><mml:mi>O</mml:mi><mml:mi>R</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="desouza-ieq3-3051559.gif"/></alternatives></inline-formula> problem to prove the proposed concept. To solve this problem, the proposed method trained a classical artificial neural network with nine weights. However, the procedure can find solutions for any number of dimensions. The results achieved demonstrate the viability of the proposal, contributing to machine learning and quantum computing researches.