MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
  • DSpace@MIT Home
  • MIT Open Access Articles
  • MIT Open Access Articles
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Quantum principal component analysis

Author(s)
Lloyd, Seth; Mohseni, Masoud; Rebentrost, Frank Patrick
Thumbnail
DownloadLloyd_Quantum principal.pdf (76.16Kb)
OPEN_ACCESS_POLICY

Open Access Policy

Creative Commons Attribution-Noncommercial-Share Alike

Terms of use
Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
Metadata
Show full item record
Abstract
The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of different observables and to analyse the results statistically. For non-sparse but low-rank quantum states, revealing eigenvectors and corresponding eigenvalues in classical form scales super-linearly with the system dimension. Here we show that multiple copies of a quantum system with density matrix ρ can be used to construct the unitary transformation e[superscript −iρt]. As a result, one can perform quantum principal component analysis of an unknown low-rank density matrix, revealing in quantum form the eigenvectors corresponding to the large eigenvalues in time exponentially faster than any existing algorithm. We discuss applications to data analysis, process tomography and state discrimination.
Date issued
2014-07
URI
http://hdl.handle.net/1721.1/97628
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering; Massachusetts Institute of Technology. Research Laboratory of Electronics
Journal
Nature Physics
Publisher
Nature Publishing Group
Citation
Lloyd, Seth, Masoud Mohseni, and Patrick Rebentrost. “Quantum Principal Component Analysis.” Nat Phys 10, no. 9 (July 27, 2014): 631–633.
Version: Original manuscript
ISSN
1745-2473
1745-2481

Collections
  • MIT Open Access Articles

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.