QUBO Formulations for Training Machine Learning Models

TL;DR

This paper formulates the training of linear regression, SVM, and k-means clustering as QUBO problems to leverage quantum computing for more efficient machine learning training, especially as classical computing faces limitations.

Contribution

It introduces novel QUBO formulations for three machine learning models, enabling their training on adiabatic quantum computers and compares their complexities to classical methods.

Findings

QUBO formulations for linear regression, SVM, and k-means clustering.

Complexity of formulations is better or equivalent to classical algorithms.

Potential for quantum computing to improve ML training efficiency.

Abstract

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.