Efficient Quantum Algorithm for Identifying Hidden Polynomials
Abstract
We consider a natural generalization of an abelian Hidden Subgroup Problem where the subgroups and their cosets correspond to graphs of linear functions over a finite field F with d elements. The hidden functions of the generalized problem are not restricted to be linear but can also be m-variate polynomial functions of total degree n>=2. The problem of identifying hidden m-variate polynomials of degree less or equal to n for fixed n and m is hard on a classical computer since Omega(sqrt{d}) black-box queries are required to guarantee a constant success probability. In contrast, we present a quantum algorithm that correctly identifies such hidden polynomials for all but a finite number of values of d with constant probability and that has a running time that is only polylogarithmic in d.
Cite
@article{arxiv.0706.1219,
title = {Efficient Quantum Algorithm for Identifying Hidden Polynomials},
author = {Thomas Decker and Jan Draisma and Pawel Wocjan},
journal= {arXiv preprint arXiv:0706.1219},
year = {2008}
}