Learning DNFs under product distributions via {\mu}-biased quantum Fourier sampling

TL;DR

This paper demonstrates that DNF formulas can be efficiently learned under product distributions using quantum algorithms, extending previous work under uniform distributions and leveraging a new quantum Fourier sampling method.

Contribution

It introduces a quantum algorithm for learning DNF formulas under {}-biased distributions, improving over classical superpolynomial time algorithms.

Findings

Quantum PAC-learning of DNF in polynomial time under product distributions

Extension of previous uniform distribution results to {}-biased distributions

Development of a new quantum Fourier sampling algorithm

Abstract

We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The best classical algorithm (without access to membership queries) runs in superpolynomial time. Our result extends the work by Bshouty and Jackson (1998) that proved that DNF formulae are efficiently learnable under the uniform distribution using a quantum example oracle. Our proof is based on a new quantum algorithm that efficiently samples the coefficients of a {\mu}-biased Fourier transform.