QUBO Formulations for Training Machine Learning Models

Training machine learning models on classical computers is usually a time and compute intensive process. With Moore's law coming to an end and ever increasing demand for large-scale data analysis using machine learning, we must leverage non-conventional computing paradigms like quantum computing to train machine learning models efficiently. Adiabatic quantum computers like the D-Wave 2000Q can approximately solve NP-hard optimization problems, such as the quadratic unconstrained binary optimization (QUBO), faster than classical computers. Since many machine learning problems are also NP-hard, we believe adiabatic quantum computers might be instrumental in training machine learning models efficiently in the post Moore's law era. In order to solve a problem on adiabatic quantum computers, it must be formulated as a QUBO problem, which is a challenging task in itself. In this paper, we formulate the training problems of three machine learning models---linear regression, support vector machine (SVM) and equal-sized k-means clustering---as QUBO problems so that they can be trained on adiabatic quantum computers efficiently. We also analyze the time and space complexities of our formulations and compare them to the state-of-the-art classical algorithms for training these machine learning models. We show that the time and space complexities of our formulations are better (in the case of SVM and equal-sized k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.