Affiliations: Dept. of Comp. Sci., Budapest Univ. of Technology and
Economics, H-1521 Budapest, Hungary. friedl@cs.bme.hu | LRI, Univ Paris-Sud, CNRS, F-91405 Orsay, France, and
CQT, Nat. Univ. of Singapore. santha@lri.fr | LRI, Univ Paris-Sud, CNRS, F-91405 Orsay, France.
magniez@lri.fr | School of Technology and Comp. Sci., Tata Institute of
Fundamental Research, Mumbai, India. pgdsen@tcs.tifr.res.in
Note: [] Address for correspondence: LRI, Univ Paris-Sud, CNRS, F-91405
Orsay, France
Abstract: 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.
