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.
Quantum algorithms for group convolution, cross-correlation, and equivariant transformations / Grecia Castelazo; Quynh T. Nguyen; Giacomo De Palma; Dirk Englund; Seth Lloyd; Bobak T. Kiani. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - ELETTRONICO. - 106:3(2022), pp. 032402.1-032402.19. [10.1103/physreva.106.032402]
Quantum algorithms for group convolution, cross-correlation, and equivariant transformations
Giacomo De Palma;
2022
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.File | Dimensione | Formato | |
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