Learning DNFs under product distributions via mu--biased quantum Fourier sampling
Varun Kanade, Andrea Rocchetto, Simone Severini · Quantum Information and Computation · 2019
We show that DNF formulae can be quantum PAC-learned in polynomial time under product distributions using a quantum example oracle. The current best classical algorithm 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 μ–biased Fourier transform.