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arXiv:2108.12448 · IEEE Transactions on Computers

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

Luciano S. de Souza, Jonathan H. A. de Carvalho, Tiago A. E. Ferreira

Published Feb 9, 2021• 14 citations
arXivHTMLPDF

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$w$-dimensional search space, where$w$is the number of weights of the neural network. To know the number of iterations requireda priorito 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$XOR$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.

DOI
10.1109/tc.2021.3051559

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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(√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 a priori the number of iterations required to obtain the solutions, unlike the classical training algorithms based on gradient descendent.
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Artificial neural networks (ANN) proved to be efficient in solving many problems for big data analytics using machine learning. The complex and non-linear features of the input data can be learned and generalized by ANN. In the big data era, enormous amounts of data arrive from multiple sources. A stage is expected to be reached where even supercomputers are likely inundated with the big data. Training an ANN in such a situation is a challenging task due to the size and dimension of the big data. Also, a large number of parameters are to be used and optimized in the network to learn the patterns and analyze such data. Quantum computing is emerging as a field that provides a solution to this problem as a quantum computer can represent data differently using qubits. Qubits on quantum computers can be used to detect the hidden patterns in data that are difficult for a classical computer to find. Hence, there exists a huge scope for application in the area of artificial neural networks. In this work, we primarily focused on training an artificial neural network using qubits as artificial neurons. The simulation results show that our quantum computing approach for ANN (QC ANN) is efficient when compared to classical ANN. The model with qubits as artificial neurons can learn the features of data using fewer parameters for a binary classification task. We demonstrate our experiment using a quantum simulator and optimization of the quantum parameters used in QC ANN is carried out on a classical computer.
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This paper investigates the potential of quantum walks to optimize deep neural networks. Traditional deep learning training relies on gradient descent methods, which can be computationally expensive and prone to getting trapped in local minima. We propose a novel approach utilizing a quantum walk algorithm to explore the loss landscape of a neural network more efficiently. The core idea involves mapping the loss surface of the network to a quantum walk environment, allowing the walker to simultaneously explore multiple possible updates, thereby increasing the chances of escaping local minima and converging to a global minimum. We formally define the quantum walk model and explore its potential advantages in terms of exploration and convergence speed. This work presents a theoretical framework and outlines a potential strategy for integrating quantum walk algorithms into the deep learning training process. The effectiveness of this approach hinges on the ability to accurately represent the complex loss surface of a deep neural network within a quantum mechanical framework.