History dependent quantum random walks as quantum lattice gas automata

Abstract

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.

Document Details

Document Type
Pub Defense Publication
Publication Date
Dec 01, 2014
Source ID
10.1063/1.4903977

Entities

People

  • Asif Shakeel
  • David A. Meyer
  • Peter J. Love

Organizations

  • Air Force Office of Scientific Research
  • Haverford College
  • National Science Foundation

Tags

Fields of Study

  • Physics

Readers

  • International Relations, focusing on Korea-Africa and North Korea-South Korea relations, and Nigeria-Latin American Relations.
  • Mathematical Modeling and Probability Theory.
  • Quantum Dot Semiconductor Device Photonics and Graphene Optoelectronic Materials and THz Physics.

Technology Areas

  • Quantum Computing