Quantum Walks on Regular Graphs and Eigenvalues

2010/11/24 by Chris Godsil, Godsil, Chris, Krystal Guo +1
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata #math.CO #quant-ph

paper · pdf · doi:10.48550/arxiv.1011.5460

openalex publication_date 2010/11/24 · arxiv created 2011/07/27 · arxiv updated 2011/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by Emms, Hancock, Severini and Wilson in 2006, that the spectrum of S⁺(U³), a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of S⁺(U) and S⁺(U²) for regular graphs.

Citations

• k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs

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