Quantum algorithms for SVD-based data representation and analysis
This work addresses the gap between theoretical quantum algorithms and practical machine learning applications, offering incremental improvements for data analysis on quantum computers.
The paper tackled the problem of applying quantum linear algebra to practical data analysis by developing quantum algorithms for SVD-based methods like PCA, achieving sublinear run-time in input size with small error and competitive classification performance in experiments.
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.