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.
Additional Metadata
Keywords quantum computing, hidden polynomials
MSC Quantum computation (msc 81P68)
THEME Logistics (theme 3)
Publisher Cornell University Library
Series arXiv.org e-Print archive
Citation
Decker, T, Draisma, J, & Wocjan, P. (2008). Quantum algorithm for identifying hidden polynomial function graphs. arXiv.org e-Print archive. Cornell University Library .