Quantum DNF Learnability Revisited

Abstract

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