Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks
Abstract
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:
-
- Univ. of Wisconsin, Madison, WI (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1259509
- Report Number(s):
- SAND2015-6076J
Journal ID: ISSN 1546-1955; SICI 1546-1955(20130701)10:7L.1653;1-
- Grant/Contract Number:
- AC04-94AL85000
- Resource 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
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Rudinger, Kenneth, Gamble, John King, Bach, Eric, Friesen, Mark, Joynt, Robert, and Coppersmith, S. N. Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks. United States: N. p., 2013.
Web. doi:10.1166/jctn.2013.3105.
Rudinger, Kenneth, Gamble, John King, Bach, Eric, Friesen, Mark, Joynt, Robert, & Coppersmith, S. N. Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks. United States. https://doi.org/10.1166/jctn.2013.3105
Rudinger, Kenneth, Gamble, John King, Bach, Eric, Friesen, Mark, Joynt, Robert, and Coppersmith, S. N. Mon .
"Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks". United States. https://doi.org/10.1166/jctn.2013.3105. https://www.osti.gov/servlets/purl/1259509.
@article{osti_1259509,
title = {Comparing Algorithms for Graph Isomorphism Using Discrete- and Continuous-Time Quantum Random Walks},
author = {Rudinger, Kenneth and Gamble, John King and Bach, Eric and Friesen, Mark and Joynt, Robert and Coppersmith, S. N.},
abstractNote = {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.},
doi = {10.1166/jctn.2013.3105},
journal = {Journal of Computational and Theoretical Nanoscience},
number = 7,
volume = 10,
place = {United States},
year = {Mon Jul 01 00:00:00 EDT 2013},
month = {Mon Jul 01 00:00:00 EDT 2013}
}
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