Quantum algorithms for group convolution, cross-correlation, and equivariant transformations
Name
PhysRevA.106.032402.pdf
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8.31 MB
Format
Adobe PDF
Checksum (MD5)
944c2aef02ef2d297eb803e1064ca92f
Author(s)
Castelazo, Grecia
Nguyen, Quynh T
De Palma, Giacomo
Englund, Dirk
Lloyd, Seth
Kiani, Bobak T
Date Issued
2022
Journal
Physical Review A
Publisher
American Physical Society
Citation
Castelazo, Grecia, Nguyen, Quynh T, De Palma, Giacomo, Englund, Dirk, Lloyd, Seth et al. 2022. "Quantum algorithms for group convolution, cross-correlation, and equivariant transformations." Physical Review A, 106 (3).
Version
Final published version
Abstract
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient quantum algorithms for performing linear group convolutions and cross-correlations on data stored as quantum states. Runtimes for our algorithms are poly-logarithmic in the dimension of the group and the desired error of the operation. Motivated by the rich literature on quantum algorithms for solving algebraic problems, our theoretical framework opens a path for quantizing many algorithms in machine learning and numerical methods that employ group operations.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
Massachusetts Institute of Technology. Department of Mechanical Engineering
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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
10.1103/physreva.106.032402
