EFFICIENT QUANTUM ALGORITHM FOR IDENTIFYING HIDDEN POLYNOMIALS

    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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