dc.contributor.author | Rebentrost, Frank | |
dc.contributor.author | Steffens, Adrian | |
dc.contributor.author | Marvian Mashhad, Iman | |
dc.contributor.author | Lloyd, Seth | |
dc.date.accessioned | 2018-03-29T18:10:36Z | |
dc.date.available | 2018-03-29T18:10:36Z | |
dc.date.issued | 2018-01 | |
dc.date.submitted | 2017-11 | |
dc.identifier.issn | 2469-9926 | |
dc.identifier.issn | 2469-9934 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/114453 | |
dc.description.abstract | We 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.publisher | American Physical Society | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1103/PhysRevA.97.012327 | en_US |
dc.rights | Article 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.source | American Physical Society | en_US |
dc.title | Quantum singular-value decomposition of nonsparse low-rank matrices | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Rebentrost, Patrick et al. "Quantum singular-value decomposition of nonsparse low-rank matrices." Physical Review A 97, 1 (January 2018): 012327 © 2018 American Physical Society | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mechanical Engineering | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Research Laboratory of Electronics | en_US |
dc.contributor.mitauthor | Rebentrost, Frank | |
dc.contributor.mitauthor | Steffens, Adrian | |
dc.contributor.mitauthor | Marvian Mashhad, Iman | |
dc.contributor.mitauthor | Lloyd, Seth | |
dc.relation.journal | Physical Review A | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2018-02-07T20:55:02Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | American Physical Society | |
dspace.orderedauthors | Rebentrost, Patrick; Steffens, Adrian; Marvian, Iman; Lloyd, Seth | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-6728-8163 | |
mit.license | PUBLISHER_POLICY | en_US |