Quantum walks on directed graphs

Details Quantum walks on directed graphs Quantum walks on directed graphs

2005-04-15

arxiv.org/abs/quant-ph/0504116v1

Quantum Information and Computation, vol. 7, no. 1 (2007)

Physics

Quantum Physics

10 pages, some xypic figures

Scientific paper

We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices (i, j), if i is connected to j then there is a path from j to i. We show that reversibility is a necessary and sufficient condition for a directed graph to allow the notion of a discrete-time quantum walk, and discuss some implications of this condition. We present a method for defining a "partially quantum" walk on directed graphs that are not reversible.

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