Quantum algorithms for testing properties of distributions

Sergey Bravyi, Aram W. Harrow, Avinatan Hassidim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

Suppose one has access to oracles generating samples from two unknown probability distributions p and q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the L1-norm? This and related questions have been extensively studied during the last years in the field of property testing. In the present paper we study quantum algorithms for testing properties of distributions. It is shown that the L1-distance ||p - q||1 can be estimated with a constant precision using only O(N1/2) queries in the quantum settings, whereas classical computers need Ω(N 1-o(1)) queries. We also describe quantum algorithms for testing Uniformity and Orthogonality with query complexity O(N1/ 3). The classical query complexity of these problems is known to be Ω(N1/2). A quantum algorithm for testing Uniformity has been recently independently discovered by Chakraborty et al [14].

Original languageEnglish
Title of host publicationSTACS 2010 - 27th International Symposium on Theoretical Aspects of Computer Science
Pages131-142
Number of pages12
DOIs
StatePublished - 2010
Externally publishedYes
Event27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010 - Nancy, France
Duration: 4 Mar 20106 Mar 2010

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume5
ISSN (Print)1868-8969

Conference

Conference27th International Symposium on Theoretical Aspects of Computer Science, STACS 2010
Country/TerritoryFrance
CityNancy
Period4/03/106/03/10

Keywords

  • Property testing
  • Quantum computing
  • Sampling

Fingerprint

Dive into the research topics of 'Quantum algorithms for testing properties of distributions'. Together they form a unique fingerprint.

Cite this