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Quantum Information Processing

The average search probabilities of discrete-time quantum walks

  • 01-09-2022
Published in:
Author
Hanmeng Zhan
Published in
Quantum Information Processing | Issue 9/2022

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Abstract

The article delves into the average search probabilities of discrete-time quantum walks on graphs, particularly focusing on distance regular graphs. It formalizes the idea of quantum walks as algorithms for searching marked vertices, tracing back to Grover's work in 1996. The study reveals that for many parametric families of distance regular graphs, the average probability of finding a marked vertex converges to 1/4 as the valency increases, regardless of other graph parameters. This surprising phenomenon is explored through spectral analysis and equitable partitions. The paper also derives conditions under which this convergence occurs, demonstrating that it applies to families of complete graphs, strongly regular graphs, and distance regular graphs of fixed parameter d. The research highlights the connection between discrete-time and continuous-time quantum walks and provides a foundation for further studies on the mixing time of quantum search algorithms on graphs.
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Title
The average search probabilities of discrete-time quantum walks
Author
Hanmeng Zhan
Publication date
01-09-2022
Publisher
Springer US
Published in
Quantum Information Processing / Issue 9/2022
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-022-03681-9
This content is only visible if you are logged in and have the appropriate permissions.

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