History dependent quantum random walks as quantum lattice gas automata

@article{Shakeel2014HistoryDQ,
  title={History dependent quantum random walks as quantum lattice gas automata},
  author={Asif Shakeel and David A. Meyer and Peter J. Love},
  journal={Journal of Mathematical Physics},
  year={2014},
  volume={55},
  pages={122204}
}
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… 

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