Singular-value decomposition using quantum annealing

TL;DR

This paper explores how quantum annealing can be used to perform singular value decomposition and principal component analysis by transforming the Hamiltonian to find maximum eigenstates.

Contribution

It introduces a novel method to perform SVD and PCA using quantum annealing through Hamiltonian sign transformation to identify maximum eigenstates.

Findings

Successfully demonstrates quantum annealing for SVD and PCA

Provides a method to estimate adiabatic time scales

Shows potential for quantum algorithms in data analysis

Abstract

In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value decomposition requires the maximum eigenstate. The key idea is to transform the sign of the final Hamiltonian, and the maximum eigenstate is obtained by quantum annealing. Furthermore, the adiabatic time scale is obtained by the approximation focusing on the maximum eigenvalue.