Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2109.00128 · Brazilian Conference on Intelligent Systems

Quantum Walk to Train a Classical Artificial Neural Network

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

Published Oct 1, 2019• 9 citations
arXivHTMLPDF

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(√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.

DOI
10.1109/bracis.2019.00149

Related papers

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

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.

arXiv:2108.12448•IEEE Transactions on Computers•Feb 9, 2021•14 citations

Quantum-Walk Based Optimization of Neural Network Weights

Jincheng Zhang

This paper investigates the potential of quantum walks for optimizing the weights within neural networks. Traditional neural network training relies heavily on classical gradient-based optimization methods, which can often get trapped in local minima and suffer from slow convergence rates. We propose a novel approach leveraging the inherent properties of quantum walks to efficiently explore the complex solution space of neural network weight optimization. The core idea involves mapping the weight update process to a quantum walk, where each walker represents a candidate weight adjustment. The walk's evolution is determined by a Hamiltonian operator constructed from the neural network's loss function. We aim to demonstrate that, under specific conditions, quantum walks can outperform classical gradient descent in terms of convergence speed and potentially escape local minima more effectively. This research represents a novel combination of quantum walk methodology with neural network optimization, offering a fundamentally different paradigm for training complex artificial intelligence models.

•Aug 28, 2026•0 citations

Quantum-Inspired Optimization of Neural Network Training Dynamics

Jincheng Zhang

Training deep neural networks remains a computationally intensive and often challenging process. Traditional optimization methods, such as stochastic gradient descent (SGD) and its variants, frequently struggle to escape local minima and converge to optimal solutions, leading to suboptimal network performance. This paper proposes a novel approach to neural network training that leverages principles inspired by quantum mechanics. Specifically, we investigate the application of quantum-inspired optimization techniques, including simulated annealing and quantum walks, to dynamically adjust the training process. The core idea is to mimic the probabilistic exploration inherent in quantum systems to effectively navigate the complex loss landscape of neural networks. We formulate the training process as a quantum-inspired optimization problem, where the network's weights are treated as quantum bits (Qubits) and the optimization algorithm seeks to find the lowest energy state, analogous to finding the minimum loss. The proposed method demonstrates the potential for accelerating convergence and improving the overall accuracy of neural networks compared to conventional optimization strategies. Our analysis focuses on the key aspects of the approach, including the mathematical formulation of the quantum-inspired optimization problem and the selection of appropriate parameters to govern the exploration and exploitation phases. We present a theoretical framework for understanding the dynamics of this approach and discuss potential avenues for further research, including hybrid quantum-classical algorithms and the integration of quantum computing hardware.

•Sep 5, 2026•0 citations

Quantum Walk-Based Optimization of Neural Network Architecture

Jincheng Zhang

This paper proposes a novel approach to neural network architecture search (NAS) leveraging the principles of quantum walks. Traditional NAS methods suffer from significant computational bottlenecks, limiting their scalability and practicality. We introduce a framework where quantum walks are employed to efficiently explore the vast architectural search space. The core idea is to map the architectural choices – such as the number of layers, the type of activation functions, and the connections between neurons – to a quantum state, allowing for parallel exploration guided by the inherent probabilistic nature of quantum walks. The algorithm iteratively evolves the quantum state, favoring architectures that maximize performance metrics (e.g., accuracy, inference time) while minimizing computational complexity. This approach offers the potential to dramatically accelerate the NAS process, enabling the discovery of high-performing neural network architectures with reduced computational cost. The theoretical framework is presented, along with a detailed explanation of the quantum walk implementation and its convergence properties. We demonstrate the feasibility and potential of this method through a series of simulations, showcasing its ability to outperform conventional NAS techniques in terms of both speed and architectural quality.

•Aug 28, 2026•0 citations

Quantum Neural Networks Learning Algorithm Based on a Global Search

Fernando M. de Paula Neto, Teresa B. Ludermir, Wilson Rosa de Oliveira

This paper reports the performance of a novel training algorithm for quantum neural networks (QNN) using a variation of the quantum search algorithm. The proposed algorithm trains a QNN exploring all possible weights with a sublinear cost. The training cost is theoretically O(√(N/t)), as a function of the quantity N of possible weights and t is the number of possible solutions. Initial experimental results demonstrate that the algorithm always converges to existing solutions, in addition to having the mean and maximum values, almost in total, lower than the expected maximum amount, as theoretically expected. The training algorithm is applied to classification problems.

Brazilian Conference on Intelligent Systems•Oct 1, 2019•4 citations

Predicting quantum advantage by quantum walk with convolutional neural networks

Alexey A. Melnikov, Leonid Evgenevich Fedichkin, Alexander Alodjants

Abstract Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical ones on certain graphs, enabling in these cases quantum algorithmic applications and quantum-enhanced energy transfer. However, little is known about the possible advantages on arbitrary graphs not having explicit symmetries. For these graphs one would need to perform simulations of classical and quantum walk dynamics to check if the speedup occurs, which could take a long computational time. Here we present a new approach for the solution of the quantum speedup problem, which is based on a machine learning algorithm that predicts the quantum advantage by just ‘looking’ at a graph. The convolutional neural network, which we designed specifically to learn from graphs, observes simulated examples and learns complex features of graphs that lead to a quantum advantage, allowing to identify graphs that exhibit quantum advantage without performing any quantum walk or random walk simulations. The performance of our approach is evaluated for line and random graphs, where classification was always better than random guess even for the most challenging cases. Our findings pave the way to an automated elaboration of novel large-scale quantum circuits utilizing quantum walk based algorithms, and to simulating high-efficiency energy transfer in biophotonics and material science.

arXiv:1901.10632•New Journal of Physics•Nov 27, 2019•45 citations
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.
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 thewww-dimensional search space, wherewwwis 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 aXORXORXORproblem 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.
This paper investigates the potential of quantum walks for optimizing the weights within neural networks. Traditional neural network training relies heavily on classical gradient-based optimization methods, which can often get trapped in local minima and suffer from slow convergence rates. We propose a novel approach leveraging the inherent properties of quantum walks to efficiently explore the complex solution space of neural network weight optimization. The core idea involves mapping the weight update process to a quantum walk, where each walker represents a candidate weight adjustment. The walk's evolution is determined by a Hamiltonian operator constructed from the neural network's loss function. We aim to demonstrate that, under specific conditions, quantum walks can outperform classical gradient descent in terms of convergence speed and potentially escape local minima more effectively. This research represents a novel combination of quantum walk methodology with neural network optimization, offering a fundamentally different paradigm for training complex artificial intelligence models.
Training deep neural networks remains a computationally intensive and often challenging process. Traditional optimization methods, such as stochastic gradient descent (SGD) and its variants, frequently struggle to escape local minima and converge to optimal solutions, leading to suboptimal network performance. This paper proposes a novel approach to neural network training that leverages principles inspired by quantum mechanics. Specifically, we investigate the application of quantum-inspired optimization techniques, including simulated annealing and quantum walks, to dynamically adjust the training process. The core idea is to mimic the probabilistic exploration inherent in quantum systems to effectively navigate the complex loss landscape of neural networks. We formulate the training process as a quantum-inspired optimization problem, where the network's weights are treated as quantum bits (Qubits) and the optimization algorithm seeks to find the lowest energy state, analogous to finding the minimum loss. The proposed method demonstrates the potential for accelerating convergence and improving the overall accuracy of neural networks compared to conventional optimization strategies. Our analysis focuses on the key aspects of the approach, including the mathematical formulation of the quantum-inspired optimization problem and the selection of appropriate parameters to govern the exploration and exploitation phases. We present a theoretical framework for understanding the dynamics of this approach and discuss potential avenues for further research, including hybrid quantum-classical algorithms and the integration of quantum computing hardware.
This paper proposes a novel approach to neural network architecture search (NAS) leveraging the principles of quantum walks. Traditional NAS methods suffer from significant computational bottlenecks, limiting their scalability and practicality. We introduce a framework where quantum walks are employed to efficiently explore the vast architectural search space. The core idea is to map the architectural choices – such as the number of layers, the type of activation functions, and the connections between neurons – to a quantum state, allowing for parallel exploration guided by the inherent probabilistic nature of quantum walks. The algorithm iteratively evolves the quantum state, favoring architectures that maximize performance metrics (e.g., accuracy, inference time) while minimizing computational complexity. This approach offers the potential to dramatically accelerate the NAS process, enabling the discovery of high-performing neural network architectures with reduced computational cost. The theoretical framework is presented, along with a detailed explanation of the quantum walk implementation and its convergence properties. We demonstrate the feasibility and potential of this method through a series of simulations, showcasing its ability to outperform conventional NAS techniques in terms of both speed and architectural quality.
This paper reports the performance of a novel training algorithm for quantum neural networks (QNN) using a variation of the quantum search algorithm. The proposed algorithm trains a QNN exploring all possible weights with a sublinear cost. The training cost is theoretically O(√(N/t)), as a function of the quantity N of possible weights and t is the number of possible solutions. Initial experimental results demonstrate that the algorithm always converges to existing solutions, in addition to having the mean and maximum values, almost in total, lower than the expected maximum amount, as theoretically expected. The training algorithm is applied to classification problems.
Abstract Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from classical random walks analogs, in particular, they walk faster than classical ones on certain graphs, enabling in these cases quantum algorithmic applications and quantum-enhanced energy transfer. However, little is known about the possible advantages on arbitrary graphs not having explicit symmetries. For these graphs one would need to perform simulations of classical and quantum walk dynamics to check if the speedup occurs, which could take a long computational time. Here we present a new approach for the solution of the quantum speedup problem, which is based on a machine learning algorithm that predicts the quantum advantage by just ‘looking’ at a graph. The convolutional neural network, which we designed specifically to learn from graphs, observes simulated examples and learns complex features of graphs that lead to a quantum advantage, allowing to identify graphs that exhibit quantum advantage without performing any quantum walk or random walk simulations. The performance of our approach is evaluated for line and random graphs, where classification was always better than random guess even for the most challenging cases. Our findings pave the way to an automated elaboration of novel large-scale quantum circuits utilizing quantum walk based algorithms, and to simulating high-efficiency energy transfer in biophotonics and material science.