Journal of Computational and Applied Mathematics

QUBO for training regression models

M. Caruso, Daniel Escánez-Expósito, Pino Caballero‐Gil, Carlos Kuchkovsky

Published Apr 2, 2026• 0 citations

Abstract

A constantly increasing number of parameters in modern machine learning models has become a significant bottleneck in their efficient training, resulting in a disproportionate consumption of resources, expressed in terms of energy and computational time. The vast majority of such resources are allocated to the training phase rather than the inference stage, leading to an inefficient process [1] , [2] , [3] . This study addresses this problem by introducing a quantum alternative for training machine learning models, formalized as a Quadratic Unconstrained Binary Optimization ( QUBO ) problem. Adiabatic quantum computers have shown promise in approximately solving certain NP -hard problems, such as QUBO , potentially offering speed advantages over classical computers in specific scenarios [ 4 , 5, [6] , [7] ]. Given that many machine learning problems are also NP -hard, adiabatic quantum computers could play a pivotal role in efficiently training machine learning models. Furthermore, inspired by the ones’ complement binary numeral system, this work includes the proposal of an efficient binary-to-decimal encoding, which improves data representation in the quantum context. A concrete implementation of a regression training problem on specific quantum hardware is also presented here, the results of which suggest that the adoption of quantum techniques in model training allows not only to address the problem of parameter explosion but also to offer promising prospects for significantly accelerate the training process by exploiting the unique properties of quantum computation.

DOI: 10.1016/j.cam.2026.117652

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