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dc.contributor.authorAaronson, Scott
dc.contributor.authorWatrous, John
dc.date.accessioned2010-03-04T18:53:22Z
dc.date.available2010-03-04T18:53:22Z
dc.date.issued2009-02
dc.date.submitted2008-08
dc.identifier.issn1471-2946
dc.identifier.issn0950-1207
dc.identifier.urihttp://hdl.handle.net/1721.1/52302
dc.description.abstractWhile closed timelike curves (CTCs) are not known to exist, studying their consequences has led to non-trivial insights into general relativity, quantum information and other areas. In this paper, we show that, if CTCs existed, quantum computers would be no more powerful than classical computers: both would have the (extremely large) power of the complexity class polynomial space (Graphic), consisting of all problems solvable by a conventional computer using a polynomial amount of memory. This solves an open problem proposed by one of us in 2005, and gives an essentially complete understanding of computational complexity in the presence of CTCs. Following the work of Deutsch, we treat a CTC as simply a region of spacetime where a ‘causal consistency’ condition is imposed, meaning that nature has to produce a (probabilistic or quantum) fixed point of some evolution operator. Our conclusion is then a consequence of the following theorem: given any quantum circuit (not necessarily unitary), a fixed point of the circuit can be (implicitly) computed in Graphic. This theorem might have independent applications in quantum information.en
dc.language.isoen_US
dc.publisherRoyal Society of Londonen
dc.relation.isversionofhttp://dx.doi.org/10.1098/rspa.2008.0350en
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en
dc.sourcearXiven
dc.titleClosed timelike curves make quantum and classical computing equivalenten
dc.typeArticleen
dc.identifier.citationAaronson, Scott, and John Watrous. “Closed timelike curves make quantum and classical computing equivalent.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 465.2102 (2009): 631-647.en
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.approverAaronson, Scott
dc.contributor.mitauthorAaronson, Scott
dc.relation.journalProceedings of the Royal Society A: Mathematical, Physical and Engineering Scienceen
dc.eprint.versionAuthor's final manuscript
dc.type.urihttp://purl.org/eprint/type/SubmittedJournalArticleen
eprint.statushttp://purl.org/eprint/status/PeerRevieweden
dspace.orderedauthorsAaronson, Scott; Watrous, Johnen
dc.identifier.orcidhttps://orcid.org/0000-0003-1333-4045
mit.licensePUBLISHER_POLICYen
mit.metadata.statusComplete


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