Two new results about quantum exact learning

09/30/2018

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by   Srinivasan Arunachalam, et al.

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We present two new results about exact learning by quantum computers. First, we show how to exactly learn a k-Fourier-sparse n-bit Boolean function from O(k^1.5( k)^2) uniform quantum examples for that function. This improves over the bound of Θ(kn) uniformly random classical examples (Haviv and Regev, CCC'15). Second, we show that if a concept class C can be exactly learned using Q quantum membership queries, then it can also be learned using O(Q^2/ Q|C|) classical membership queries. This improves the previous-best simulation result (Servedio and Gortler, SICOMP'04) by a Q-factor.