  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.
