Quantum testers for hidden group properties

Details Quantum testers for hidden group properties Quantum testers for hidden group properties

2002-08-29

arxiv.org/abs/quant-ph/0208184v1

Physics

Quantum Physics

11 pages

Scientific paper

We construct efficient or query efficient quantum property testers for two existential group properties which have exponential query complexity both for their decision problem in the quantum and for their testing problem in the classical model of computing. These are periodicity in groups and the common coset range property of two functions having identical ranges within each coset of some normal subgroup. Our periodicity tester is efficient in Abelian groups and generalizes, in several aspects, previous periodicity testers. This is achieved by introducing a technique refining the majority correction process widely used for proving robustness of algebraic properties. The periodicity tester in non-Abelian groups and the common coset range tester are query efficient.

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