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Quantum Information and Computation     ISSN: 1533-7146      published since 2001
Vol.19 No.15&16 December 2019  

Learning DNFs under product distributions via mu--biased quantum Fourier sampling (pp1261-1278)
          
Varun Kanade, Andrea Rocchetto, and Simone Severini
         
doi: https://doi.org/10.26421/QIC19.15-16-1
Abstracts: 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 mu--biased Fourier transform.
Key words:
quantum learning theory, PAC model, Fourier analysis

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