Quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs (preliminary version)


We study quantum algorithms for testing properties of sparse graphs. Let G be a boundeddegree graph on N vertices. Given an oracle that answers queries of the form “what is the ith neighbor of vertex v?”, the problem is to distinguish whether G is bipartite or far from bipartite. A result of Goldreich and Ron shows that the classical query complexity of… (More)