EFFICIENT QUANTUM ALGORITHM FOR IDENTIFYING HIDDEN POLYNOMIALS
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(root 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.
Quantum Information & Computation
"EFFICIENT QUANTUM ALGORITHM FOR IDENTIFYING HIDDEN POLYNOMIALS" (2009). Faculty Bibliography 2000s. 1465.