Controlling quantum random walk with a step-dependent coin

S Panahiyan,S Fritzsche

doi:10.1088/1367-2630/aad899

S Panahiyan, S Fritzsche

Open Access

https://doi.org/10.1088/1367-2630/aad899

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Abstract

We report on the possibility of controlling quantum random walks (QWs) with a step-dependent coin (SDC). The coin is characterized by a (single) rotation angle. Considering different rotation angles, one can find diverse probability distributions for this walk including: complete localization, Gaussian and asymmetric likes. In addition, we explore the entropy of walk in two contexts; for probability density distributions over position space and walker's internal degrees of freedom space (coin space). We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. In general, we demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC.

Highlights

Classical random walks (CWs) are known processes that have been used for developing stochastic algorithms [1], in studying biological behavior [2], for image segmentation [3] as well as in earthquake simulations [4]
We studied a class of quantum random walk (QW) with a step-dependent coin (SDC)
We studied the entropy of walks with the SDC and compare it with its corresponding step-independent coin (SIC) case

Summary

August 2018

Original content from this work may be used under the terms of the Creative Abstract. Considering different rotation angles, this work must maintain attribution to the one can find diverse probability distributions for this walk including: complete localization, Gaussian author(s) and the title of and asymmetric likes. We show that entropy of position space can decrease for a SDC with the step-number, quite in contrast to a walk with step-independent coin (SIC). For entropy of coin space, a damped oscillation is found for walk with SIC while for a SDC case, the behavior of entropy depends on rotation angle. We demonstrate that quantum walks with simple initiatives may exhibit a quite complex and varying behavior if SDCs are applied. This provides the possibility of controlling QW with a SDC

Introduction

QW with SDC

Simulation of the walk

Experimental implementation

Shannon entropy

Conclusion