Affiliation:
1. Institute of Theoretical Computer Science, Ulm University, D-89069 Ulm, Germany
Abstract
We provide an exact quantum query algorithm that identifies uncorrupted codewords from a degree-d generalized Reed-Muller code of length qn over the finite field of size q. When d is constant, the algorithm needs 𝒪(nd-1) quantum queries, which is optimal. Classically, Ω(nd) queries are necessary to accomplish this task, even with constant probability of error admitted. Our work extends a result by Montanaro about learning multilinear polynomials.
Publisher
World Scientific Pub Co Pte Lt
Subject
Computer Science (miscellaneous)