2012/12/18 by Peter P. Rohde, Gavin K. Brennen, Alexei Gilchrist
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Computer science #Dimension (graph theory) #Function (biology) #Mathematics #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum entanglement #Quantum mechanics #Quantum walk #Random walk #Randomness #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.87.052302
published as Phys. Rev. A, 87, 052302 (2013)
arxiv created 2012/12/18 · openalex publication_date 2013/05/02 · arxiv updated 2013/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observe several phenomena. First in one dimension, walkers with memory have persistent quantum ballistic speed up over classical walks just as found in previous studies of multicoined walks with trivial memory function. However, measurement of the multicoin state can dramatically shift the mean of the spatial distribution. Second, we consider spatial entanglement in a two-dimensional quantum walk with memory and find that memory destroys entanglement between the spatial dimensions, even when entangling coins are employed. Finally, we explore behavior in the presence of spatial randomness and find that in the time regime where single-coined walks localize, multicoined walks do not and in fact a memory function can speed up the walk relative to a multicoin walker with no memory. We explicitly show how to construct linear optics circuits implementing the walks, and discuss prospects for classical simulation.