A mixed-precision quantum-classical algorithm for solving linear systems

TL;DR

This paper introduces a hybrid quantum-classical algorithm that enhances the efficiency of solving linear systems by combining low-precision quantum solutions with iterative refinement, reducing quantum resource requirements.

Contribution

It proposes a novel mixed-precision iterative refinement method for QSVT-based linear solvers, improving accuracy and reducing quantum resource consumption.

Findings

The algorithm achieves higher accuracy with fewer quantum resources.

Error and complexity analysis demonstrate efficiency gains.

Preliminary experiments validate the approach using myQLM.

Abstract

We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy. To reduce the quantum cost, we propose a hybrid quantum-classical algorithm that improves the accuracy and reduces the cost of the QSVT by adding iterative refinement in mixed-precision A first quantum solution is computed using the QSVT, in low precision, and then refined in higher precision until we get a satisfactory accuracy. For this solver, we present an error and complexity analysis, and first experiments using the quantum software stack myQLM.