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Title: Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks

Berry and Wang [Phys. Rev. A 83, 042317 (2011)] show numerically that a discrete-time quan- tum random walk of two noninteracting particles is able to distinguish some non-isomorphic strongly regular graphs from the same family. Here we analytically demonstrate how it is possible for these walks to distinguish such graphs, while continuous-time quantum walks of two noninteracting parti- cles cannot. We show analytically and numerically that even single-particle discrete-time quantum random walks can distinguish some strongly regular graphs, though not as many as two-particle noninteracting discrete-time walks. Additionally, we demonstrate how, given the same quantum random walk, subtle di erences in the graph certi cate construction algorithm can nontrivially im- pact the walk's distinguishing power. We also show that no continuous-time walk of a xed number of particles can distinguish all strongly regular graphs when used in conjunction with any of the graph certi cates we consider. We extend this constraint to discrete-time walks of xed numbers of noninteracting particles for one kind of graph certi cate; it remains an open question as to whether or not this constraint applies to the other graph certi cates we consider.
Authors:
 [1] ;  [1] ;  [1] ;  [1] ;  [1] ;  [1]
  1. Univ. of Wisconsin, Madison, WI (United States)
Publication Date:
Report Number(s):
SAND2015-6076J
Journal ID: ISSN 1546-1955; SICI 1546-1955(20130701)10:7L.1653;1-
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
Journal of Computational and Theoretical Nanoscience
Additional Journal Information:
Journal Volume: 10; Journal Issue: 7; Journal ID: ISSN 1546-1955
Publisher:
American Scientific Publishers
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1259509