Title

EFFICIENT QUANTUM ALGORITHM FOR IDENTIFYING HIDDEN POLYNOMIALS

Authors

Authors

T. Decker; J. Draisma;P. Wocjan

Comments

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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(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.

Journal Title

Quantum Information & Computation

Volume

9

Issue/Number

3-4

Publication Date

1-1-2009

Document Type

Article

First Page

215

Last Page

230

WOS Identifier

WOS:000264937400003

ISSN

1533-7146

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