Quantum DNF Learnability Revisited
We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of ~O(s3/∈ + s 2/∈ 2), where s is the size of DNF formula and ∈ is the PAC error accuracy. If s and 1/∈ are comparable, this gives a modest improvement over a previously known classical query complexity of Õ(ns 2 /te 2). We also show a lower bound of Ω(slogn/n on the query complexity of any quantum PAC algorithm for learning a DNF of size s with n inputs under the uniform distribution.
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