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DOI: 10.4230/LIPIcs.TQC.2018.3
URN: urn:nbn:de:0030-drops-92501
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9250/
Belovs, Aleksandrs ; Rosmanis, Ansis
Quantum Lower Bounds for Tripartite Versions of the Hidden Shift and the Set Equality Problems
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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.The 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.
The lower bounds are proven by a novel application of the dual learning graph framework and by using representation-theoretic tools from [Belovs, 2018].
BibTeX - Entry
@InProceedings{belovs_et_al:LIPIcs:2018:9250,
author = {Aleksandrs Belovs and Ansis Rosmanis},
title = {{Quantum Lower Bounds for Tripartite Versions of the Hidden Shift and the Set Equality Problems}},
booktitle = {13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018)},
pages = {3:1--3:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-080-4},
ISSN = {1868-8969},
year = {2018},
volume = {111},
editor = {Stacey Jeffery},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9250},
URN = {urn:nbn:de:0030-drops-92501},
doi = {10.4230/LIPIcs.TQC.2018.3},
annote = {Keywords: Adversary Bound, Dual Learning Graphs, Quantum Query Complexity, Representation Theory}
}
| Keywords: | Adversary Bound, Dual Learning Graphs, Quantum Query Complexity, Representation Theory | |
| Seminar: | 13th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 16.07.2018 |
