Zero transfer in continuous-time quantum walks

A. Sett, H. Pan, P. E. Falloon, J. B. Wang

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Abstract

In this paper, we show how using complex-valued edge weights in a graph can completely suppress the flow of probability amplitude in a continuous-time quantum walk to specific vertices of the graph when the edge weights, graph topology, and initial state of the quantum walk satisfy certain conditions. The conditions presented in this paper are derived from the so-called chiral quantum walk, a variant of the continuous-time quantum walk which incorporates directional bias with respect to site transfer probabilities between vertices of a graph by using complex edge weights. We examine the necessity to break the time-reversal symmetry in order to achieve zero transfer in continuous-time quantum walks. We also consider the effect of decoherence on zero transfer and suggest that this phenomenon may be used to detect and quantify decoherence in the system.

Original languageEnglish
Article number159
Number of pages18
JournalQuantum Information Processing
Volume18
Issue number5
DOIs
Publication statusPublished - May 2019

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