The quantum query complexity of learning multilinear polynomials
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 boundederror classical algorithm for this task requires Omega(n^d) queries to the polynomial. We give an exact quantum algorithm that uses O(n^(d1)) queries for constant d, which is optimal. In the case q=2, this gives a quantum algorithm that uses O(n^(d1)) queries to identify a codeword picked from the binary ReedMuller code of order d.
 Publication:

arXiv eprints
 Pub Date:
 May 2011
 arXiv:
 arXiv:1105.3310
 Bibcode:
 2011arXiv1105.3310M
 Keywords:

 Quantum Physics
 EPrint:
 8 pages