2016/11/22 by Asif Shakeel, Shakeel, Asif
Physics and Astronomy · #68Q12 #68Q80 #FOS: Physical sciences #Quantum Physics (quant-ph) #msc:68Q12 #msc:68Q80 #quant-ph
paper · pdf · doi:10.48550/arxiv.1611.07495
17 pages, 11 figures, reorganized and with changes to explanatory text. Phys. Scr. version
arxiv created 2019/06/17 · arxiv updated 2019/06/19
History dependent discrete time quantum walks (QWs) are often studied for their lattice traversal properties. A particular model in the literature uses the state of a memory qubit at each site to record visits and to control the dynamics of the walk. We generalize this model to the neighborhood-history quantum walk (NHQW), in which the walk dynamics and the state of the memory qubits in a neighborhood of the particle's position are interdependent. To demonstrate it, we construct an NHQW on a one-dimensional lattice, with a simple neighborhood. Several dynamically interesting history dependent QWs can be realized as single-particle sectors of quantum lattice gas automata (QLGA). In contrast, the NHQW constructed in this paper is realized as a single-particle sector of the more general quantum cellular automaton (QCA). The complexity of the NHQW dynamics presents a promising avenue toward richer walk strategies and a potentially useful model of QWs for the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing. It also modifies QWs to conceivably allow for modeling fundamental physics incorporating quantum field interactions with particles.