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Title: History dependent quantum random walks as quantum lattice gas automata

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice.
Authors:
;  [1] ;  [2]
  1. Department of Physics, Haverford College, Haverford, Pennsylvania 19041 (United States)
  2. Department of Mathematics, University of California/San Diego, La Jolla, California 92093-0112 (United States)
Publication Date:
OSTI Identifier:
22403068
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DEGREES OF FREEDOM; GRAPH THEORY; PARTICLES; RANDOMNESS; SPIN