Spatial search by continuous-time quantum walk with multiple marked vertices

Spatial search by continuous-time quantum walk with multiple marked vertices In the typical spatial search problems solved by continuous-time quantum walk, changing the location of the marked vertices does not alter the search problem. In this paper, we consider search when this is no longer true. In particular, we analytically solve search on the “simplex of $$K_M$$ K M complete graphs” with all configurations of two marked vertices, two configurations of $$M+1$$ M + 1 marked vertices, and two configurations of $$2(M+1)$$ 2 ( M + 1 ) marked vertices, showing that the location of the marked vertices can dramatically influence the required jumping rate of the quantum walk, such that using the wrong configuration’s value can cause the search to fail. This sensitivity to the jumping rate is an issue unique to continuous-time quantum walks that does not affect discrete-time ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Spatial search by continuous-time quantum walk with multiple marked vertices

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1239-y
Publisher site
See Article on Publisher Site

Abstract

In the typical spatial search problems solved by continuous-time quantum walk, changing the location of the marked vertices does not alter the search problem. In this paper, we consider search when this is no longer true. In particular, we analytically solve search on the “simplex of $$K_M$$ K M complete graphs” with all configurations of two marked vertices, two configurations of $$M+1$$ M + 1 marked vertices, and two configurations of $$2(M+1)$$ 2 ( M + 1 ) marked vertices, showing that the location of the marked vertices can dramatically influence the required jumping rate of the quantum walk, such that using the wrong configuration’s value can cause the search to fail. This sensitivity to the jumping rate is an issue unique to continuous-time quantum walks that does not affect discrete-time ones.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 25, 2016

References

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