dc.contributor.author | Aaronson, Scott | |
dc.date.accessioned | 2012-08-09T15:27:20Z | |
dc.date.available | 2012-08-09T15:27:20Z | |
dc.date.issued | 2011-01 | |
dc.identifier.issn | 1433-8092 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/72073 | |
dc.description.abstract | We show that any quantum algorithm to decide whether a function f:\left[n\right] \rightarrow\left[ n\right] is a permutation or far from a permutation\ must make \Omega\left( n^{1/3}/w\right) queries to f, even if the algorithm is given a w-qubit quantum witness in support of f being a permutation. This implies that there exists an oracle A such that \mathsfSZKA\mathsfQMAA , answering an eight-year-old open question of the author. Indeed, we show that relative to some oracle, \mathsfSZK is not in the counting class \mathsfA\mathsf0\mathsfPP defined by Vyalyi. The proof is a fairly simple extension of the quantum lower bound for the collision problem.. | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (grant 0844626) | en_US |
dc.description.sponsorship | United States. Defense Advanced Research Projects Agency (YFA grant) | en_US |
dc.language.iso | en_US | |
dc.publisher | Hasso-Plattner-Institut für Softwaresystemtechnik GmbH | en_US |
dc.relation.isversionof | http://eccc.hpi-web.de/report/2011/001/ | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
dc.source | MIT web domain | en_US |
dc.title | Impossibility of Succinct Quantum Proofs for Collision-Freeness | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Aaronson, Scott. "Impossibility of Succinct Quantum Proofs for Collision-Freeness." Electronic Colloquium on Computational Complexity (2011): TR11-001. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | en_US |
dc.contributor.approver | Aaronson, Scott | |
dc.contributor.mitauthor | Aaronson, Scott | |
dc.relation.journal | Electronic Colloquium on Computational Complexity | en_US |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dspace.orderedauthors | Aaronson, Scott | en_US |
dc.identifier.orcid | https://orcid.org/0000-0003-1333-4045 | |
mit.license | OPEN_ACCESS_POLICY | en_US |
mit.metadata.status | Complete | |