Quantum DNF Learnability Revisited

Abstract

We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of Õ (s3/ε + s2/ε2), where s is the size of DNF formula and ε is the PAC error accuracy1. If s and 1/ε are comparable, this gives a modest improvement over a previously known classical query complexity of Õ(ns2/ε2). We also show a lower bound of Ω(s log n/n) on the query complexity of any quantum PAC algorithm for learning a DNF of size s with n inputs under the uniform distribution.