Quantum principal component analysis
Name
Lloyd_Quantum principal.pdf
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Author(s)
Lloyd, Seth
Mohseni, Masoud
Rebentrost, Frank Patrick
Date Issued
July 2014
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1038/nphys3029
