Quantum DNF Learnability Revisited

Abstract

We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\tilde{O}(s^{3}/\epsilon + s^{2}/\epsilon^{2})$, where $s$ is the size of DNF formula and $\epsilon$ is the PAC error accuracy. If $s$ and $1/\epsilon$ are comparable, this gives a modest improvement over a previously known classical query complexity of $\tilde{O}(ns^{2}/\epsilon^{2})$. We also show a lower bound of $\Omega(s\log n/n)$ on the query complexity of any quantum PAC algorithm for learning a DNF of size $s$ with $n$ inputs under the uniform distribution.