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Coherence as resource in scattering quantum walk search on complete graph

Authors :
Yun-Long Su
Si-Yuan Liu
Xiao-Hui Wang
Heng Fan
Wen-Li Yang
Source :
Scientific Reports, Vol 8, Iss 1, Pp 1-13 (2018)
Publication Year :
2018
Publisher :
Nature Portfolio, 2018.

Abstract

Abstract We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is significantly larger than the marked number of vertices we are searching, N ≫ v. We find that the consumption of coherence represents the increase of the success probability for the searching, also it is related to the efficiency of the algorithm in oracle queries. If no coherence is consumed or an incoherent state is utilized, the algorithm will behave as the classical blind search, implying that coherence is responsible for the speed-up in this quantum algorithm over its classical counterpart. The effect of noises, in particular of photon loss and random phase shifts, on the performance of algorithm is studied. Two types of noise are considered because they arise in the optical network used for experimental realization of scattering quantum walk. It is found that photon loss will reduce the coherence and random phase shifts will hinder the interference between the edge states, both leading to lower success probability compared with the noise-free case. We then conclude that coherence plays an essential role and is responsible for the speed-up in this quantum algorithm.

Subjects

Subjects :
Medicine
Science

Details

Language :
English
ISSN :
20452322
Volume :
8
Issue :
1
Database :
Directory of Open Access Journals
Journal :
Scientific Reports
Publication Type :
Academic Journal
Accession number :
edsdoj.ba37c018f8834aca8409ae57da2155fa
Document Type :
article
Full Text :
https://doi.org/10.1038/s41598-018-29342-5