Quantum Physics
[Submitted on 8 Jun 2007 (v1), last revised 2 Sep 2008 (this version, v3)]
Title:Efficient Quantum Algorithm for Identifying Hidden Polynomials
View PDFAbstract: 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.
Submission history
From: Pawel Wocjan [view email][v1] Fri, 8 Jun 2007 17:44:20 UTC (11 KB)
[v2] Wed, 2 Apr 2008 17:41:14 UTC (16 KB)
[v3] Tue, 2 Sep 2008 15:54:39 UTC (17 KB)
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