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Journal of Applied Mathematics

A Novel Algorithm of Quantum Random Walk in Server Traffic Control and Task Scheduling

Dong Yumin, Xiao Shufen

Published Jan 1, 2014• 4 citations
Publisher

Abstract

A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one m -dimensional quantum random walk into m one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm), ACO (ant colony optimization), and SAA (simulated annealing algorithm). In the same time, we prove its validity and rationality by the experiment of analog and simulation.

DOI
10.1155/2014/818479

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A quantum random walk optimization model and algorithm in network cluster server traffic control and task scheduling is proposed. In order to solve the problem of server load balancing, we research and discuss the distribution theory of energy field in quantum mechanics and apply it to data clustering. We introduce the method of random walk and illuminate what the quantum random walk is. Here, we mainly research the standard model of one-dimensional quantum random walk. For the data clustering problem of high dimensional space, we can decompose one m -dimensional quantum random walk into m one-dimensional quantum random walk. In the end of the paper, we compare the quantum random walk optimization method with GA (genetic algorithm), ACO (ant colony optimization), and SAA (simulated annealing algorithm). In the same time, we prove its validity and rationality by the experiment of analog and simulation.
Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithms and overcomes some limitations of the traditional ACO algorithm. However, due to the hardware resource limitations of currently available quantum computers, such as the limited number of qubits, lack of high-fidelity gating operation, and low noisy tolerance, the practical application of the QACO is quite challenging. In this paper, we introduce a hybrid quantum-classical algorithm by combining the clustering algorithm with QACO algorithm, so that this extended QACO can handle large-scale optimization problems, which makes the practical application of QACO based on available quantum computation resource possible. To verify the effectiveness and performance of the algorithm, we tested the developed QACO algorithm with the Travelling Salesman Problem (TSP) as benchmarks. The developed QACO algorithm shows better performance under multiple data set. In addition, the developed QACO algorithm also manifests the robustness to noise of calculation process, which is typically a major barrier for practical application of quantum computers. Our work shows that the combination of the clustering algorithm with QACO has effectively extended the application scenario of QACO in current NISQ era of quantum computing.
This paper investigates the application of quantum-inspired concepts to enhance the performance of random walk algorithms for optimization problems. Classical random walk algorithms are susceptible to getting trapped in local optima, limiting their efficacy in tackling complex and high-dimensional search spaces. To address this limitation, we propose a novel approach that incorporates principles of quantum superposition and tunneling into the random walk process. The algorithm leverages these concepts to enable more extensive exploration of the search space, thereby increasing the probability of converging towards the global optimum. We present a detailed formulation of the algorithm, outlining the key parameters and their influence on the optimization process. The theoretical analysis demonstrates the potential advantages of this quantum-inspired approach compared to traditional random walk methods. The algorithm's ability to escape local minima is evaluated through simulations, showcasing its effectiveness in a variety of benchmark optimization problems. The results highlight the promise of quantum-inspired techniques in improving the robustness and efficiency of random walk algorithms, offering a viable strategy for solving challenging optimization tasks.
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science. Furthermore, in quantum mechanics, quantum walks can be regarded as quantum analogues of classical random walks. Classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding. In this article, we aim to provide a comprehensive review of classical random walks and quantum walks. We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms. We also compare the algorithms based on quantum walks and classical random walks from the perspective of time complexity. Then we introduce their applications in the field of computer science. Finally we discuss the open issues from the perspectives of efficiency, main-memory volume, and computing time of existing algorithms. This study aims to contribute to this growing area of research by exploring random walks and quantum walks together.
The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one dimensional QRW. Then, the probability distributions on the positions induced by QRW in these algorithms are investigated, which also indicates the possibility of obtaining better results. Consequently, the experimental results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms are of fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.
Aiming at the disadvantage of optimization problems based on traditional ant colony optimization (ACO)which easily falls into local optimums and has worse performance in convergence,the paper unifies the quantum evolutionary algorithm (QEA) and the ant colony algorithm,in this algorithm,pheromone is represented by quantum bits and updated by a new quantum rotation gate adjustment srrategy.And this paper applies separately this algorithm and the traditional ACO to traveling salesman problem(TSP),The simulation results show that the algorithm of this paper has excellent global optimization properties and quicker convergence than the traditional ACO.
The logistics distribution route problem is a NP problem which possesses important practical value. A novel optimization method of logistics distribution route is proposed based on Quantum Ant Colony Algorithm(QACA)to overcome the problems such as long computing time and easy to fall into local best for traditional heuristic optimization algorithm. The optimization problem of logistics distribution routing is analyzed, and the mathematical model is established, and then the quantum ant colony algorithm is used to solve it, and the pheromone on each path is encoded by a group of quantum bits,and a new pheromone representation is designed,called quantum pheromone, and the quantum rotation gate and the best tour are applied to updating the pheromone. The simulation test is carried out to test the performance of QACA. The simulation results show that, QACA has a strong global search ability and convergence speed, and can effectively solve the logistics distribution routing problem.