{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article11280","name":"Quantum Lower Bounds for Tripartite Versions of the Hidden Shift and the Set Equality Problems","abstract":"In this paper, we study quantum query complexity of the following rather natural tripartite generalisations (in the spirit of the 3-sum problem) of the hidden shift and the set equality problems, which we call the 3-shift-sum and the 3-matching-sum problems.\nThe 3-shift-sum problem is as follows: given a table of 3 x n elements, is it possible to circularly shift its rows so that the sum of the elements in each column becomes zero? It is promised that, if this is not the case, then no 3 elements in the table sum up to zero. The 3-matching-sum problem is defined similarly, but it is allowed to arbitrarily permute elements within each row. For these problems, we prove lower bounds of Omega(n^{1\/3}) and Omega(sqrt n), respectively. The second lower bound is tight.\nThe lower bounds are proven by a novel application of the dual learning graph framework and by using representation-theoretic tools from [Belovs, 2018].","keywords":["Adversary Bound","Dual Learning Graphs","Quantum Query Complexity","Representation Theory"],"author":[{"@type":"Person","name":"Belovs, Aleksandrs","givenName":"Aleksandrs","familyName":"Belovs","affiliation":"Faculty of Computing, University of Latvia, Raina 19, Riga, Latvia","funding":"This research is partially supported by the ERDF project number 1.1.1.2\/I\/16\/113. Part of this work was done while supported by the ERC Advanced Grant MQC."},{"@type":"Person","name":"Rosmanis, Ansis","givenName":"Ansis","familyName":"Rosmanis","affiliation":"Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore","funding":"This research is partially funded by the Singapore Ministry of Education and the National Research Foundation under grant R-710-000-012-135."}],"position":3,"pageStart":"3:1","pageEnd":"3:15","dateCreated":"2018-07-16","datePublished":"2018-07-16","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Belovs, Aleksandrs","givenName":"Aleksandrs","familyName":"Belovs","affiliation":"Faculty of Computing, University of Latvia, Raina 19, Riga, Latvia","funding":"This research is partially supported by the ERDF project number 1.1.1.2\/I\/16\/113. Part of this work was done while supported by the ERC Advanced Grant MQC."},{"@type":"Person","name":"Rosmanis, Ansis","givenName":"Ansis","familyName":"Rosmanis","affiliation":"Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, Singapore","funding":"This research is partially funded by the Singapore Ministry of Education and the National Research Foundation under grant R-710-000-012-135."}],"copyrightYear":"2018","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.TQC.2018.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","citation":"http:\/\/arxiv.org\/abs\/1506.08106","isPartOf":{"@type":"PublicationVolume","@id":"#volume6314","volumeNumber":111,"name":"13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)","dateCreated":"2018-07-16","datePublished":"2018-07-16","editor":{"@type":"Person","name":"Jeffery, Stacey","givenName":"Stacey","familyName":"Jeffery"},"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article11280","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":"#volume6314"}}}