Andrew Bressler ; Robin Pemantle - Quantum random walks in one dimension via generating functions

dmtcs:3533 - Discrete Mathematics & Theoretical Computer Science, January 1, 2007, DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07) - https://doi.org/10.46298/dmtcs.3533
Quantum random walks in one dimension via generating functionsArticle

Authors: Andrew Bressler 1; Robin Pemantle 1

  • 1 Department of Mathematics [Philadelphia]

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.


Volume: DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
Section: Proceedings
Published on: January 1, 2007
Imported on: May 10, 2017
Keywords: Hadamard,asymptotics,rational generating function,[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]
Funding:
    Source : OpenAIRE Graph
  • Asymptotic enumeration, reinforcement, and effective limit theory; Funder: National Science Foundation; Code: 0603821

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