Year: 2011
Type: preprint
Abstract: In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omega(n^d) queries to the polynomial. We give an exact quantum algorithm that uses O(n^(d-1)) queries for constant d, which is optimal. In the case q=2, this gives a quantum algorithm that uses O(n^(d-1)) queries to identify a codeword picked from the binary Reed-Muller code of order d.
Source: arXiv (Cornell University)
Author: Montanaro, Ashley
Institution: University of Cambridge
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952561065