2003/05/06 by Arul Lakshminarayan, Lakshminarayan, Arul
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Condensed Matter (cond-mat) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #cond-mat #nlin.CD #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0305026
14 pgs, 6 figures, Revtex4
arxiv created 2003/05/06 · openalex publication_date 2003/05/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As an example of an integrable coin we study the Fourier walk that generalizes the Hadamard walk and show that the walker slows down with coin dimensionality, which controls the effective Planck constant. Introducing multi-Harper maps as deterministic models of random walks we study the effect of coin chaos on the quantum walk. We also demonstrate that breaking time-reversal symmetry in the coin dynamics effectively slows down the walk.