Faster transport with a directed quantum walk

Stephan Hoyer and David A. Meyer

Phys. Rev. A 79, 024307 – Published 18 February 2009

Abstract

We give an example of faster transport with a quantum walk on an inherently directed graph, on the directed line with a variable number of self-loops at each vertex. These self-loops can be thought of as adding a number of small dimensions. This is a discrete time quantum walk using the Fourier transform coin, where the walk proceeds a distance $Θ (1)$ in constant time compared to $Θ (1 / n)$ classically, independent of the number of these small dimensions. The analysis proceeds by reducing this walk to a walk with a two-dimensional coin.

Received 9 January 2009

DOI:https://doi.org/10.1103/PhysRevA.79.024307

Authors & Affiliations

Stephan Hoyer^* and David A. Meyer^†

Department of Mathematics, University of California–San Diego, San Diego, California 92093, USA

^*Author to whom correspondence should be addressed. Present address: Department of Physics, University of California, Berkeley, CA 94720, USA; shoyer@berkeley.edu
^†dmeyer@math.ucsd.edu

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Vol. 79, Iss. 2 — February 2009

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