Circuit Implementation of Discrete-Time Quantum Walks on Complex Networks

TL;DR

This paper introduces a novel quantum circuit design for implementing discrete-time quantum walks on complex networks, enabling practical applications in graph analysis.

Contribution

It provides the first specific quantum circuit design for quantum walks on complex networks, demonstrated with Watts-Strogatz models.

Findings

Circuit accurately simulates quantum walks on Watts-Strogatz networks.

Comparison with theoretical calculations validates the circuit's functionality.

Abstract

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.