Quantum property testing for sparse graphs
|Affiliation:||University of Waterloo|
|Room:||Mathematics & Computer Building (MC) 5158|
In property testing, the goal is to determine whether an object has a certain property or is far from having that property. Many properties of graphs can be tested very quickly, even classically; for example, one can decide whether a graph is connected or far from connected in constant time, independent of the size of the graph. However, Goldreich and Ron showed that testing bipartiteness or expansion of n-vertex graphs requires at least about sqrt(n) queries. By derandomizing classical property testing algorithms and applying quantum techniques for collision finding, we show that these problems can be solved in only about n1/3 steps on a quantum computer. Whether quantum algorithms might offer an exponential speedup for testing graph properties remains an interesting open question.
This is joint work with Yi-Kai Liu (Caltech).
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