Separating quantum and classical learning

Abstract

We consider a model of learning Boolean functions from quantum membership queries. This model was studied in [26], where it was shown that any class of Boolean functions which is informationtheoretically learnable from polynomially many quantum membership queries is also information-theoretically learnable from polynomially many classical membership queries. In this paper we establish a strong computational separation between quantum and classical learning. We prove that if any cryptographic oneway function exists, then there is a class of Boolean functions which is polynomial-time learnable from quantum membership queries but not polynomial-time learnable from classical membership queries. A novel consequence of our result is a quantum algorithm that breaks a general cryptographic construction which is secure in the classical setting. © 2011 Springer-Verlag Berlin Heidelberg.