dc.contributor.author | Aaronson, Scott | |
dc.contributor.author | Ambainis, Andris | |
dc.contributor.author | Balodis, Kaspars | |
dc.contributor.author | Bavarian, Mohammad | |
dc.date.accessioned | 2015-11-02T17:16:49Z | |
dc.date.available | 2015-11-02T17:16:49Z | |
dc.date.issued | 2014 | |
dc.identifier.isbn | 978-3-662-43947-0 | |
dc.identifier.isbn | 978-3-662-43948-7 | |
dc.identifier.issn | 0302-9743 | |
dc.identifier.issn | 1611-3349 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/99645 | |
dc.description.abstract | We study the query complexity of Weak Parity: the problem of computing the parity of an n-bit input string, where one only has to succeed on a 1/2 + ε fraction of input strings, but must do so with high probability on those inputs where one does succeed. It is well-known that n randomized queries and n/2 quantum queries are needed to compute parity on all inputs. But surprisingly, we give a randomized algorithm for Weak Parity that makes only O(n/log[superscript 0.246](1/ε)) queries, as well as a quantum algorithm that makes O(n/√log(1/ε)) queries. We also prove a lower bound of Ω(n/log(1/ε)) in both cases, as well as lower bounds of Ω(logn) in the randomized case and Ω(√logn) in the quantum case for any ε > 0. We show that improving our lower bounds is intimately related to two longstanding open problems about Boolean functions: the Sensitivity Conjecture, and the relationships between query complexity and polynomial degree. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant 0844626) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Alan T. Waterman Award) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.). Science and Technology Center (Award 0939370) | en_US |
dc.language.iso | en_US | |
dc.publisher | Springer-Verlag | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1007/978-3-662-43948-7_3 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Weak Parity | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Aaronson, Scott, Andris Ambainis, Kaspars Balodis, and Mohammad Bavarian. “Weak Parity.” Lecture Notes in Computer Science (2014): 26–38. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Aaronson, Scott | en_US |
dc.contributor.mitauthor | Bavarian, Mohammad | en_US |
dc.relation.journal | Automata, Languages, and Programming | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/ConferencePaper | en_US |
eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
dspace.orderedauthors | Aaronson, Scott; Ambainis, Andris; Balodis, Kaspars; Bavarian, Mohammad | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-3292-2520 | |
dc.identifier.orcid | https://orcid.org/0000-0003-1333-4045 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |