Quantum walk with a general coin: exact solution and asymptotic properties

Quantum walk with a general coin: exact solution and asymptotic properties In this paper, we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on the line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either remain put in the place or proceed in a fixed direction but never move backward, although they can be easily modified to describe the case in which the particle can travel in both directions. We use these expressions to explore properties of magnitudes associated to the process, as the probability mass function or the probability current, even though we also consider the asymptotic behavior of the exact solution. Within this approximation, we will estimate upper and lower bounds, examine the origins of an emerging approximate symmetry, and deduce the general form of the stationary probability density of the relative location of the walker. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum walk with a general coin: exact solution and asymptotic properties

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Publisher
Springer Journals
Copyright
Copyright © 2014 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/s11128-014-0908-6
Publisher site
See Article on Publisher Site

Abstract

In this paper, we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on the line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either remain put in the place or proceed in a fixed direction but never move backward, although they can be easily modified to describe the case in which the particle can travel in both directions. We use these expressions to explore properties of magnitudes associated to the process, as the probability mass function or the probability current, even though we also consider the asymptotic behavior of the exact solution. Within this approximation, we will estimate upper and lower bounds, examine the origins of an emerging approximate symmetry, and deduce the general form of the stationary probability density of the relative location of the walker.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jan 7, 2015

References

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