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International Conference on Advanced Computing and Communication Systems (ICACCS)

Quantum Walk Circuits to Analyze Networks

Anurag Kumar Singh, Binshumesh Sachan

Published Mar 25, 2022• 0 citations
Publisher

Abstract

Quantum walks are studied extensively using various networks. The quantum version of the walk involves using the properties found in quantum computing. These properties can include quantum interference, no-cloning theorem, and restriction on an intermediate measurement. Here, in the proposed work, we focus on finding out the properties associated with the networks using quantum walks while also verifying its findings. One of the properties includes identifying critical nodes in a network vital for its robustness and survivability. So, the results related to this and some other properties are analyzed. The proposed work requires the implementation of quantum walk on different networks. Therefore, this research paper presents an algorithm that takes an undirected network,$G$, as input and constructs the quantum circuit to perform quantum walk on$G$. The working of the proposed algorithm is shown using various networks, from simple to complex.

DOI
10.1109/icaccs54159.2022.9785059

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Quantum walks are studied extensively using various networks. The quantum version of the walk involves using the properties found in quantum computing. These properties can include quantum interference, no-cloning theorem, and restriction on an intermediate measurement. Here, in the proposed work, we focus on finding out the properties associated with the networks using quantum walks while also verifying its findings. One of the properties includes identifying critical nodes in a network vital for its robustness and survivability. So, the results related to this and some other properties are analyzed. The proposed work requires the implementation of quantum walk on different networks. Therefore, this research paper presents an algorithm that takes an undirected network,GGG, as input and constructs the quantum circuit to perform quantum walk onGGG. The working of the proposed algorithm is shown using various networks, from simple to complex.
Some interesting findings can be achieved by modeling and visualizing networks which can include complex networks and large scale networks to name a few. These networks have been analyzed with the help of classical stochastic walks before. So, here in our proposed work, we provide the quantum version of the walk which basically involves making use of properties found in quantum computing. These properties can include such as quantum interference, no-cloning theorem, and restriction on intermediate measurement. In this proposed work, we present quantum circuit designs for discrete time random walk algorithms that operate on various networks.To demonstrate our ideas we have considered two different types of networks, the star network and an extended version of the star network.Though there exist a few research works related to quantum approach for random walk on networks, to the best of our knowledge, the ideas and approach we present here are unique. These ideas which we have discussed can be extended to more complex networks and systems as well. As an application of quantum walk we have shown, how results got after performing quantum walk can be used to identify critical nodes in such networks. Therefore, we have also provided some analysis of complex networks. Identification of critical nodes is important for robustness and survivability of the network.
In this paper, we propose a circuit design for implementing quantum walks on complex networks. Quantum walks are powerful tools for various graph-based applications such as spatial search, community detection, and node classification. Although many quantum-walk-based graph algorithms have been extensively studied, specific quantum circuits for implementing these algorithms have not yet been provided. To address this issue, we present a circuit design for implementing the discrete-time quantum walk on complex networks. We investigate the functionality of our circuit using the small-sized Watts-and-Strogatz model as the complex network model, comparing it with theoretical calculations. This work offers a new approach to constructing quantum circuits for implementing quantum walks on arbitrary complex networks.
This book explores the intersection of quantum computing and network science. It bridges the theoretical foundations of quantum walk algorithms with their applications in the structural exploration and representation learning of complex networks. Quantum walks, a technology that is pivotal to universal quantum computational models, examines the movement of particles on a graph composed of nodes and links. Quantum superposition enables these particles to traverse these graphs more quickly, while measurement-induced collapse introduces fluctuations, making the identification of critical nodes challenging yet intriguing. At its core, the book explores how quantum walk algorithms can transform the structural and representational analysis of complex networks. It begins by introducing the fundamental concepts of quantum computing and quantum walks, including generalized definitions and the properties of low-dimensional quantum walks. Then, it discusses the implementation of discrete- and continuous-time quantum walks for mining network nodes, links, and subgraphs, as well as their use in network representation learning and graph neural networks. The book will serve as a valuable reference for researchers, students, and educators interested in quantum walks, complex networks, quantum mechanics, and information engineering.
This paper investigates the application of quantum walks to the design of routing protocols for computer networks. Traditional routing algorithms, reliant on classical probability and exhaustive search, often suffer from inefficiencies and vulnerabilities, particularly in large and complex network topologies. Quantum walks, leveraging the principles of superposition and interference, offer a fundamentally different approach. This research proposes a framework for encoding network topologies within a quantum walk environment and utilizing the walk's inherent properties to explore the network and identify optimal paths. The core of the approach lies in mapping network nodes to quantum bits (Qubits) and utilizing the walk's probabilistic nature to simulate path exploration. We explore key aspects of this approach, including walk initialization, boundary conditions, and measurement strategies. The potential benefits of this method, such as reduced latency, improved bandwidth utilization, and enhanced resilience to network disruptions, are discussed. We present a theoretical model for the routing protocol and analyze its performance characteristics, focusing on metrics like path length, traversal time, and success rate. While this work is primarily a theoretical exploration, it lays a foundation for future research and development of practical quantum routing solutions.
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This paper investigates the application of quantum walks to network security analysis, specifically focusing on graph traversal algorithms for anomaly detection and vulnerability assessment. Traditional graph traversal methods often struggle with the complexity of large and dynamic network topologies. Quantum walks, leveraging superposition and interference, offer a potentially more efficient approach. We propose a framework utilizing quantum walks to systematically explore network graphs, identifying patterns and deviations from normal behavior that may indicate malicious activity. The core idea is to represent network nodes and edges as quantum states and utilize the walk's propagation to efficiently discover anomalous routes or node behaviors. We formally define the quantum walk algorithm, including the Hamiltonian operator, initial state preparation, and measurement process. The theoretical analysis demonstrates the potential for exponential speedups in certain scenarios compared to classical graph traversal algorithms. This work lays the groundwork for a novel approach to network security, capitalizing on the inherent advantages of quantum computing for complex pattern recognition and anomaly detection. The key contributions are the formalized quantum walk algorithm for graph traversal and an analysis of its potential advantages.