Quantum Walk to Train a Classical Artificial Neural Network

TL;DR

This paper introduces a quantum walk-based method to train classical neural networks, leveraging quantum speedup for weight search while reducing computational costs by only adjusting output layer weights.

Contribution

It presents a novel quantum walk approach for neural network training that is faster and allows pre-determination of iteration count, inspired by Extreme Learning Machine.

Findings

Quantum walk search is quadratically faster than classical search.

Variance of quantum walk is $O(t)$, classical is $O(\sqrt{t})$.

Method reduces training computational cost and predicts iteration count.

Abstract

This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to simulate a quantum machine to execute the quantum walk. In this way, to minimize the computational cost, the methodology employed to train the neural network will adjust the synaptic weights of the output layer, not altering the weights of the hidden layer, inspired in the method of Extreme Learning Machine. The quantum walk algorithm as a search algorithm is quadratically faster than its classic analog. The quantum walk variance is $O(t)$ while the variance of its classic analog is $O(\sqrt{t})$, where $t$ is the time or iteration. In addition to computational gain, another advantage of the proposed procedure is to be possible to know \textit{a priori} the number of iterations required to obtain the solutions, unlike the classical training algorithms based on gradient descendent.