History dependent quantum random walks as quantum lattice gas automata

摘要: Quantum Random Walks (QRW) were first defined as one-particle sectors of Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states position states. These models the goal studying transition classicality, more generally, changes in performance quantum walks algorithmic applications. We show that several dependent QRW can be identified QLGA. This provides a unifying conceptual framework for these which extra degrees freedom required store information arise naturally geometrical lattice.