Quantum algorithms for SVD-based data representation and analysis

TL;DR

This paper develops quantum algorithms that significantly speed up data analysis tasks like PCA and LSA, demonstrating their efficiency and accuracy through theoretical analysis and simulated experiments.

Contribution

It introduces new quantum algorithms for eigenproblem solutions in data analysis that are sublinear in input size, with proven error bounds and practical simulation results.

Findings

Algorithms run in sublinear time relative to input size.

Simulated PCA achieves competitive classification accuracy.

Error bounds are tight and well-characterized.

Abstract

This 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.