A Quantum Computational Learning Algorithm
Abstract
An interesting classical result due to Jackson allows polynomial-time learning of the function class DNF using membership queries. Since in most practical learning situations access to a membership oracle is unrealistic, this paper explores the possibility that quantum computation might allow a learning algorithm for DNF that relies only on example queries. A natural extension of Fourier-based learning into the quantum domain is presented. The algorithm requires only an example oracle, and it runs in O(sqrt(2^n)) time, a result that appears to be classically impossible. The algorithm is unique among quantum algorithms in that it does not assume a priori knowledge of a function and does not operate on a superposition that includes all possible states.
Cite
@article{arxiv.quant-ph/9807052,
title = {A Quantum Computational Learning Algorithm},
author = {Dan Ventura and Tony Martinez},
journal= {arXiv preprint arXiv:quant-ph/9807052},
year = {2007}
}
Comments
This is a reworked and improved version of a paper originally entitled "Quantum Harmonic Sieve: Learning DNF Using a Classical Example Oracle"