Abstract
AbstractThis paper narrows the gap between previous literature on quantum linear algebra and practical data analysis on a quantum computer, formalizing quantum procedures that speed-up the solution of eigenproblems for data representations in machine learning. The power and practical use of these subroutines is shown through new quantum algorithms, sublinear in the input matrix’s size, for principal component analysis, correspondence analysis, and latent semantic analysis. We provide a theoretical analysis of the run-time and prove tight bounds on the randomized algorithms’ error. We run experiments on multiple datasets, simulating PCA’s dimensionality reduction for image classification with the novel routines. The results show that the run-time parameters that do not depend on the input’s size are reasonable and that the error on the computed model is small, allowing for competitive classification performances.
Funder
National Research Foundation Singapore
Horizon 2020 Framework Programme
Association Nationale de la Recherche et de la Technologie
Politecnico di Milano
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Artificial Intelligence,Computational Theory and Mathematics,Theoretical Computer Science,Software
Cited by
5 articles.
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