Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension
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LIPIcs-ISAAC-2020-47.pdf
Description
Published version
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561.27 KB
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Adobe PDF
Checksum (MD5)
38293625150df7eb9708b5708a40fcec
Author(s)
Chia, NH
Gilyén, A
Lin, HH
Lloyd, S
Tang, E
Wang, C
Date Issued
December 1, 2020
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Citation
Chia, NH, Gilyén, A, Lin, HH, Lloyd, S, Tang, E et al. 2020. "Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension." Leibniz International Proceedings in Informatics, LIPIcs, 181.
Version
Final published version
Abstract
We present two efficient classical analogues of the quantum matrix inversion algorithm [16] for low-rank matrices. Inspired by recent work of Tang [27], assuming length-square sampling access to input data, we implement the pseudoinverse of a low-rank matrix allowing us to sample from the solution to the problem Ax = b using fast sampling techniques. We construct implicit descriptions of the pseudo-inverse by finding approximate singular value decomposition of A via subsampling, then inverting the singular values. In principle, our approaches can also be used to apply any desired “smooth” function to the singular values. Since many quantum algorithms can be expressed as a singular value transformation problem [15], our results indicate that more low-rank quantum algorithms can be effectively “dequantised” into classical length-square sampling algorithms.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Physics
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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/10.4230/LIPIcs.ISAAC.2020.47
