Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension

Nai Hui Chia, András Gilyén, Han Hsuan Lin, Seth Lloyd, Ewin Tang, Chunhao Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publication31st International Symposium on Algorithms and Computation, ISAAC 2020
EditorsYixin Cao, Siu-Wing Cheng, Minming Li
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages471-4717
Number of pages4247
ISBN (Electronic)9783959771733
DOIs
StatePublished - Dec 2020
Event31st International Symposium on Algorithms and Computation, ISAAC 2020 - Virtual, Hong Kong, China
Duration: Dec 14 2020Dec 18 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume181
ISSN (Print)1868-8969

Conference

Conference31st International Symposium on Algorithms and Computation, ISAAC 2020
CountryChina
CityVirtual, Hong Kong
Period12/14/2012/18/20

All Science Journal Classification (ASJC) codes

  • Software

Fingerprint Dive into the research topics of 'Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension'. Together they form a unique fingerprint.

Cite this