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  1. Home > Articles & Issues >
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  3. Quantum random walks ...
Conference paper

Quantum random walks in one dimension via generating functions

Andrew Bressler (1), Robin Pemantle (1)
(1) Department of Mathematics [Philadelphia]
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Imported on
May 10, 2017
Published on
December 31, 2006
Last modified on
March 31, 2025
Volume
DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
Proceedings
DOI
10.46298/dmtcs.3533
License
https://about.hal.science/hal-authorisation-v1
National Science Foundation
0603821
Asymptotic enumeration, reinforcement, and effective limit theory
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658
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1063
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Quantum random walks in one dimension via generating functions

Andrew Bressler (1), Robin Pemantle (1)
(1) Department of Mathematics [Philadelphia]
Abstract
We analyze nearest neighbor one-dimensional quantum random walks with arbitrary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known phenomenon, namely that the walk has linear speed rather than the diffusive behavior observed in classical random walks. We also obtain exact formulae for the leading asymptotic term of the wave function and the location probabilities.
Keywords
  • [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
  • [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]
  • Hadamard
  • asymptotics
  • rational generating function
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