eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-07-04
16:1
16:15
10.4230/LIPIcs.ICALP.2019.16
article
Two New Results About Quantum Exact Learning
Arunachalam, Srinivasan
1
Chakraborty, Sourav
2
Lee, Troy
3
Paraashar, Manaswi
2
de Wolf, Ronald
4
Center for Theoretical Physics, MIT, Cambridge, MA, USA
Indian Statistical Institute, Kolkata, India
Centre for Quantum Software and Information, School of Software, Faculty of Engineering and Information Technology, University of Technology Sydney, Australia
QuSoft, CWI and University of Amsterdam, The Netherlands
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}(log k)^2) uniform quantum examples for that function. This improves over the bound of Theta~(kn) uniformly random classical examples (Haviv and Regev, CCC'15). Our main tool is an improvement of Chang’s lemma for sparse Boolean functions. 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}/{log Q} * log|C|) classical membership queries. This improves the previous-best simulation result (Servedio-Gortler, SICOMP'04) by a log Q-factor.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol132-icalp2019/LIPIcs.ICALP.2019.16/LIPIcs.ICALP.2019.16.pdf
quantum computing
exact learning
analysis of Boolean functions
Fourier sparse Boolean functions