1 research outputs found
On learning linear functions from subset and its applications in quantum computing
Let be the finite field of size and let be a linear function. We introduce the {\em
Learning From Subset} problem LFS of learning , given samples from a special distribution depending on : the
probability of sampling is a function of and is non zero for at
most values of . We provide a randomized algorithm for
LFS with sample complexity and running time polynomial
in and . Our algorithm generalizes and improves upon
previous results \cite{Friedl, Ivanyos} that had provided algorithms for
LFS with running time . We further present
applications of our result to the {\em Hidden Multiple Shift} problem
HMS in quantum computation where the goal is to determine the hidden
shift given oracle access to shifted copies of an injective function
, that is we can make queries of the form
where can assume possible values. We reduce
HMS to LFS to obtain a polynomial time algorithm for
HMS when is prime and . The best known
algorithms \cite{CD07, Friedl} for HMS with these parameters require
exponential time.Comment: 20 pages, short version to appear in proceedings of ESA 201