Quantum singular-value decomposition of nonsparse low-rank matrices
Name
PhysRevA.97.012327.pdf
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172.67 KB
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Checksum (MD5)
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Author(s)
Rebentrost, Frank
Steffens, Adrian
Marvian Mashhad, Iman
Lloyd, Seth
Date Issued
January 2018
Journal
Physical Review A
Publisher
American Physical Society
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
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Research Laboratory of Electronics
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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.
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DOI of Published Version
https://doi.org/10.1103/PhysRevA.97.012327
