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Related Experiment Video

Updated: Jul 4, 2025

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

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Published on: April 8, 2020

A parameter-independent algorithm of finding maximum clique with Seidel continuous-time quantum walks.

Xi Li^1,2, Xiao Chen^1,2, Shouwei Hu^1,2

¹School of Computer Science and Engineering, Southeast University, No.2, Sipailou District, Nanjing, Jiangsu 210096, China.

|February 9, 2024

Summary

This study introduces a new parameter-independent algorithm for finding the maximum clique (MC) in network analysis. Continuous-time quantum walks (CTQW) using the Seidel matrix offer stable and effective MC identification.

Keywords:

Physics Quantum physics

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Area of Science:

Quantum Computing
Network Analysis
Graph Theory

Background:

The maximum clique (MC) problem is crucial in network analysis.
Current quantum algorithms for MC are parameter-dependent and vary across graphs.

Purpose of the Study:

To develop a stable, parameter-independent algorithm for identifying the maximum clique.
To explore the efficacy of continuous-time quantum walks (CTQW) driven by the Seidel matrix for MC detection.

Main Methods:

In-depth analysis of CTQW on four graph types, calculating vertex amplitudes.
Utilizing the Seidel matrix for CTQW, outperforming the adjacency matrix approach.
Developing a novel parameter-independent algorithm based on probability amplitude intensities.

Main Results:

Vertices in the maximum clique consistently show highest intensity at the largest frequency component of probability amplitudes.
The proposed algorithm demonstrates greater stability compared to a typical quantum-based algorithm.
CTQW driven by the Seidel matrix provides superior insights into graph clique structures.

Conclusions:

The Seidel matrix-driven CTQW is a promising tool for understanding graph clique structures.
The developed parameter-independent algorithm offers a stable and effective method for MC identification.
This approach advances quantum algorithms for complex network analysis problems.