Adaptive Learning for Quantum Linear Regression

TL;DR

This work tackles the challenge of solving linear regression with quantum annealing by casting the problem as a QUBO and encoding real-valued coefficients with a precision vector. It introduces an adaptive, per-weight precision strategy, updating the coefficients’ precision vectors iteratively to improve fit quality, and evaluates both simulated-annealing and quantum-annealing solvers on increasingly large synthetic datasets using the D-Wave Advantage. Results show that adaptive precision (SA-Ada, QA-Ada) yields consistently better $R^2$ than nonadaptive encodings, at the cost of longer runtimes, and demonstrate the largest linear-regression-on-quantum-annealer tests to date. The findings highlight practical gains and remaining hardware-driven limitations (qubit count, connectivity) and point to future directions in embeddings and advanced annealing techniques to make quantum linear regression more competitive in real-world settings.

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.

Figures (1)

• Figure 1: Logarithmic plot of time--to--solution (TTS) of linear regression evaluated on the datasets in Table \ref{['tab:reg']}.