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Quantum algorithms for group convolution, cross-correlation, and equivariant transformations

Author(s)
Castelazo, Grecia; Nguyen, Quynh T; De Palma, Giacomo; Englund, Dirk; Lloyd, Seth; Kiani, Bobak T; ... Show more Show less
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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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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.
Date issued
2022
URI
https://hdl.handle.net/1721.1/153940
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
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

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