Percolation induced effects in two-dimensional coined quantum walks: Analytic asymptotic solutions

B. Kollár, J. Novotný, T. Kiss, I. Jex

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the long-time behaviour appears untreatable with direct numerical methods. We develop novel analytic methods based on the theory of random unitary operations which help us to determine explicitly the asymptotic dynamics of quantum walks on two-dimensional finite integer lattices with percolation. Based on this theory, we find new unexpected features of percolated walks like asymptotic position inhomogeneity or special directional symmetry breaking.

Original languageEnglish
Article number023002
JournalNew Journal of Physics
Volume16
DOIs
Publication statusPublished - Feb 1 2014

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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