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

Abstract

This paper 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 required \textit{a priori} 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 $XOR$ 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.

arXiv comment19 pages, 7 figures

References in corpus (15)

• Quantum Machine Learning
• Quantum Amplitude Amplification and Estimation
• A Quantum Random Walk Search Algorithm
• Quantum walks: a comprehensive review
• Tight bounds on quantum searching
• Metaheuristic Design of Feedforward Neural Networks: A Review of Two Decades of Research
• Quantum algorithms for supervised and unsupervised machine learning
• Quantum-enhanced machine learning
• Simulating a perceptron on a quantum computer
• Quantum Perceptron Models
• Grover Search with Lackadaisical Quantum Walks
• Faster Search by Lackadaisical Quantum Walk
• The quantum walk search algorithm: Factors affecting efficiency
• Quantum Walk to Train a Classical Artificial Neural Network
• Quantum Circuit Design for Training Perceptron Models

Cited by in corpus (5)

• Review on Quantum Walk Computing: Theory, Implementation, and Application
• On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids
• Lackadaisical quantum walk in the hypercube to search for multiple marked vertices
• Quantum walk-based protocol for secure communication between any two directly connected nodes on a network
• Decoding Quantum Search Advantage: The Critical Role of State Properties in Random Walks