Quantum walks on general graphs

Abstract

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.

8 pages, v2: substantial rewrite improves clarity, corrects errors and omissions; v3: removes major error in final section and integrates remainder into other sections, figures removed