{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6800","name":"New Results on Quantum Property Testing","abstract":"We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing.\r\n\r\nFirst, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\\to[m]$. Here the probability $P_f(j)$ of an outcome $j$ in $[m]$ is the fraction of its domain that $f$ maps to $j$. We give quantum algorithms for testing whether two such distributions are identical or $epsilon$-far in $L_1$-norm. Recently, Bravyi, Hassidim, and Harrow showed that if \r\n$P_f$ and $P_g$ are both unknown (i.e., given by oracles $f$ and $g$), then this testing can be done in roughly $sqrt{m}$ quantum queries to the functions. We consider the case where the second distribution is known, and show that testing can be done with roughly $m^{1\/3}$ quantum queries, which we prove to be essentially optimal. In contrast, it is known that classical testing algorithms need about $m^{2\/3}$ queries in the unknown-unknown case and about $sqrt{m}$ queries in the known-unknown case. Based on this result, we also reduce the query complexity of graph isomorphism testers with quantum oracle access.\r\n\r\nWhile those examples provide polynomial quantum speed-ups, our third example gives a much larger improvement (constant quantum queries vs polynomial classical queries) for the problem of testing periodicity, based on Shor's algorithm and a modification of a classical lower bound by Lachish and Newman. This provides an alternative to a recent constant-vs-polynomial speed-up due to Aaronson.","keywords":["quantum algorithm","property testing"],"author":[{"@type":"Person","name":"Chakraborty, Sourav","givenName":"Sourav","familyName":"Chakraborty"},{"@type":"Person","name":"Fischer, Eldar","givenName":"Eldar","familyName":"Fischer"},{"@type":"Person","name":"Matsliah, Arie","givenName":"Arie","familyName":"Matsliah"},{"@type":"Person","name":"de Wolf, Ronald","givenName":"Ronald","familyName":"de Wolf"}],"position":12,"pageStart":145,"pageEnd":156,"dateCreated":"2010-12-14","datePublished":"2010-12-14","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Chakraborty, Sourav","givenName":"Sourav","familyName":"Chakraborty"},{"@type":"Person","name":"Fischer, Eldar","givenName":"Eldar","familyName":"Fischer"},{"@type":"Person","name":"Matsliah, Arie","givenName":"Arie","familyName":"Matsliah"},{"@type":"Person","name":"de Wolf, Ronald","givenName":"Ronald","familyName":"de Wolf"}],"copyrightYear":"2010","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2010.145","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6211","volumeNumber":8,"name":"IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)","dateCreated":"2010-12-13","datePublished":"2010-12-13","editor":[{"@type":"Person","name":"Lodaya, Kamal","givenName":"Kamal","familyName":"Lodaya"},{"@type":"Person","name":"Mahajan, Meena","givenName":"Meena","familyName":"Mahajan"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6800","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6211"}}}