Adaptive Learning for Quantum Linear Regression

TL;DR

This paper introduces an adaptive encoding method for quantum annealing in linear regression, improving solution quality by tuning precision vectors per coefficient, tested on large datasets with promising results.

Contribution

It presents a novel adaptive precision encoding approach for quantum linear regression, enhancing solution accuracy on large datasets using quantum annealers.

Findings

Improved solution quality across all tested instances.

Largest dataset evaluated for quantum annealed linear regression.

Potential for better exploitation of current quantum devices.

Abstract

The recent availability of quantum annealers as cloud-based services has enabled new ways to handle machine learning problems, and several relevant algorithms have been adapted to run on these devices. In a recent work, linear regression was formulated as a quadratic binary optimization problem that can be solved via quantum annealing. Although this approach promises a computational time advantage for large datasets, the quality of the solution is limited by the necessary use of a precision vector, used to approximate the real-numbered regression coefficients in the quantum formulation. In this work, we focus on the practical challenge of improving the precision vector encoding: instead of setting an array of generic values equal for all coefficients, we allow each one to be expressed by its specific precision, which is tuned with a simple adaptive algorithm. This approach is evaluated on synthetic datasets of increasing size, and linear regression is solved using the D-Wave Advantage quantum annealer, as well as classical solvers. To the best of our knowledge, this is the largest dataset ever evaluated for linear regression on a quantum annealer. The results show that our formulation is able to deliver improved solution quality in all instances, and could better exploit the potential of current quantum devices.