2007/05/31 by B. L. Douglas, Brendan L Douglas, J. B. Wang +1 · 3 citations
Computer Science · Physics and Astronomy · #Complexity and Algorithms in Graphs #Machine Learning and Algorithms #Quantum Computing Algorithms and Architecture #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/7/075303
published as J. Phys. A: Math. Theor. 41 (2008) 075303
openalex publication_date 2008/02/05 · arxiv created 2008/03/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
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.