A classical approach to the graph isomorphism problem using quantum walks

Brendan L. Douglas*, Jingbo B. Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

95 Citations (Scopus)


Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such algorithms have been scarce. In this work, we enumerate some important differences between quantum and classical walks, leading to their markedly different properties. We show that for many practical purposes, the implementation of quantum walks can be efficiently achieved using a classical computer. We then develop both classical and quantum graph isomorphism algorithms based on discrete-time quantum walks. We show that they are effective in identifying isomorphism classes of large databases of graphs, in particular groups of strongly regular graphs. We consider this approach to represent a promising candidate for an efficient solution to the graph isomorphism problem, and believe that similar methods employing quantum walks, or derivatives of these walks, may prove beneficial in constructing other algorithms for a variety of purposes.

Original languageEnglish
Article number075303
Pages (from-to)1-15
Number of pages15
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
Publication statusPublished - 22 Feb 2008
Externally publishedYes


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