How viable is quantum annealing for solving linear algebra problems?

TL;DR

This paper evaluates the potential of quantum annealing for solving linear algebra problems, using simulations and proposing a hybrid quantum-classical approach to improve solution quality.

Contribution

It provides new insights into quantum annealing's robustness and scalability for linear algebra, and introduces a hybrid method combining quantum annealing with classical iteration.

Findings

Quantum annealing is robust against ill-conditioned systems.

Quantum annealing scales well with system size.

Hybrid quantum-classical methods can improve solutions.

Abstract

With the increasing popularity of quantum computing and in particular quantum annealing, there has been growing research to evaluate the meta-heuristic for various problems in linear algebra: from linear least squares to matrix and tensor factorization. At the core of this effort is to evaluate quantum annealing for solving linear least squares and linear systems of equations. In this work, we focus on the viability of using quantum annealing for solving these problems. We use simulations based on the adiabatic principle to provide new insights for previously observed phenomena with the D-wave machines, such as quantum annealing being robust against ill-conditioned systems of equations and scaling quite well against the number of rows in a system. We then propose a hybrid approach which uses a quantum annealer to provide a initial guess of the solution $x_0$, which would then be iteratively improved with classical fixed point iteration methods.