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Quantum
Information and Computation
ISSN: 1533-7146
published since 2001
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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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