Search algorithm on strongly regular graphs based on scattering quantum walks

• Published in: 中国物理B：英文版 Vol. 26; no. 1; pp. 108 - 114
• Main Author: 薛希玲 刘志昊 陈汉武
• Format: Journal Article
• Language: English
• Published: 2017
• Subjects: Meyer; 图搜索算法; 强正则图; 搜索空间; 散射; 时间量子; 矩阵摄动理论; 连续时间
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/26/1/010301

Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs（SRGs） with parameters（N, k, λ, μ） achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm＇s performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O（√N） time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.