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

Journal Article · Mon Jul 01 00:00:00 EDT 2013 · Journal of Computational and Theoretical Nanoscience

DOI:https://doi.org/10.1166/jctn.2013.3105· OSTI ID:1259509

Rudinger, Kenneth ^[1]; Gamble, John King ^[1]; Bach, Eric ^[1]; Friesen, Mark ^[1]; Joynt, Robert ^[1]; Coppersmith, S. N. ^[1]

---

1. Univ. of Wisconsin, Madison, WI (United States)

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.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1259509
• Report Number(s): SAND2015-6076J; SICI 1546-1955(20130701)10:7L.1653; 1-
• Journal Information: Journal of Computational and Theoretical Nanoscience, Vol. 10, Issue 7; ISSN 1546-1955
• Publisher: American Scientific Publishers
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING