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dc.contributor.authorRebentrost, Frank
dc.contributor.authorSteffens, Adrian
dc.contributor.authorMarvian Mashhad, Iman
dc.contributor.authorLloyd, Seth
dc.date.accessioned2018-03-29T18:10:36Z
dc.date.available2018-03-29T18:10:36Z
dc.date.issued2018-01
dc.date.submitted2017-11
dc.identifier.issn2469-9926
dc.identifier.issn2469-9934
dc.identifier.urihttp://hdl.handle.net/1721.1/114453
dc.description.abstractWe present a method to exponentiate nonsparse indefinite low-rank matrices on a quantum computer. Given access to the elements of the matrix, our method allows one to determine the singular values and their associated singular vectors in time exponentially faster in the dimension of the matrix than known classical algorithms. The method extends to non-Hermitian and nonsquare matrices via matrix embedding. Moreover, our method preserves the phase relations between the singular spaces allowing for efficient algorithms that require operating on the entire singular-value decomposition of a matrix. As an example of such an algorithm, we discuss the Procrustes problem of finding a closest isometry to a given matrix.en_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevA.97.012327en_US
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_US
dc.sourceAmerican Physical Societyen_US
dc.titleQuantum singular-value decomposition of nonsparse low-rank matricesen_US
dc.typeArticleen_US
dc.identifier.citationRebentrost, Patrick et al. "Quantum singular-value decomposition of nonsparse low-rank matrices." Physical Review A 97, 1 (January 2018): 012327 © 2018 American Physical Societyen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mechanical Engineeringen_US
dc.contributor.departmentMassachusetts Institute of Technology. Research Laboratory of Electronicsen_US
dc.contributor.mitauthorRebentrost, Frank
dc.contributor.mitauthorSteffens, Adrian
dc.contributor.mitauthorMarvian Mashhad, Iman
dc.contributor.mitauthorLloyd, Seth
dc.relation.journalPhysical Review Aen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2018-02-07T20:55:02Z
dc.language.rfc3066en
dc.rights.holderAmerican Physical Society
dspace.orderedauthorsRebentrost, Patrick; Steffens, Adrian; Marvian, Iman; Lloyd, Sethen_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-6728-8163
mit.licensePUBLISHER_POLICYen_US


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