License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2019.16
URN: urn:nbn:de:0030-drops-105929
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10592/
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Arunachalam, Srinivasan ; Chakraborty, Sourav ; Lee, Troy ; Paraashar, Manaswi ; de Wolf, Ronald

Two New Results About Quantum Exact Learning

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LIPIcs-ICALP-2019-16.pdf (0.5 MB)

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
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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