Abstract of Paper

Quantum testers for hidden group properties
by Katalin Friedl, Frederic Magniez, Miklos Santha, Pranab Sen

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.