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DOI: 10.4230/LIPIcs.ICALP.2019.16
URN: urn:nbn:de:0030-drops-105929
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10592/
Arunachalam, Srinivasan ; Chakraborty, Sourav ; Lee, Troy ; Paraashar, Manaswi ; de Wolf, Ronald
Two New Results About Quantum Exact Learning
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Abstract
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.
BibTeX - Entry
@InProceedings{arunachalam_et_al:LIPIcs:2019:10592,
author = {Srinivasan Arunachalam and Sourav Chakraborty and Troy Lee and Manaswi Paraashar and Ronald de Wolf},
title = {{Two New Results About Quantum Exact Learning}},
booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
pages = {16:1--16:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-109-2},
ISSN = {1868-8969},
year = {2019},
volume = {132},
editor = {Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10592},
URN = {urn:nbn:de:0030-drops-105929},
doi = {10.4230/LIPIcs.ICALP.2019.16},
annote = {Keywords: quantum computing, exact learning, analysis of Boolean functions, Fourier sparse Boolean functions}
}
| Keywords: | quantum computing, exact learning, analysis of Boolean functions, Fourier sparse Boolean functions | |
| Seminar: | 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) | |
| Issue date: | 2019 | |
| Date of publication: | 04.07.2019 |
