Quantum vs. classical walks with memory two

Jing-Feng Wu, Peng Xu, Xuanmin Zhu

Qing Zhou, Songfeng Lu

Dan Li, Michael Mc Gettrick, Yu‐Guang Yang +2 more

Michael Mc Gettrick, Jarosław Adam Miszczak

Peter P. Rohde, Gavin K. Brennen, Alexei Gilchrist

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.

Zlatko Dimcovic, Yevgeniy Kovchegov

We construct a quantum interchange walk, related to classical walks with memory. This gives us a coinless discrete walk, while the origin in classical walks with memory offers the promise of use of existing tools from classical memoried walks. This approach readily reproduces all standard approaches. We briefly discuss its generality and advantages.