QUBO formulations for training machine learning models
Abstract
Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an 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 can approximately solve NP-hard 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 problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.
- Authors:
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities Division
- OSTI Identifier:
- 1833737
- Alternate Identifier(s):
- OSTI ID: 1784155
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Published Article
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Name: Scientific Reports Journal Volume: 11 Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Computer science; Information theory and computation
Citation Formats
Date, Prasanna, Arthur, Davis, and Pusey-Nazzaro, Lauren. QUBO formulations for training machine learning models. United Kingdom: N. p., 2021.
Web. doi:10.1038/s41598-021-89461-4.
Date, Prasanna, Arthur, Davis, & Pusey-Nazzaro, Lauren. QUBO formulations for training machine learning models. United Kingdom. https://doi.org/10.1038/s41598-021-89461-4
Date, Prasanna, Arthur, Davis, and Pusey-Nazzaro, Lauren. Tue .
"QUBO formulations for training machine learning models". United Kingdom. https://doi.org/10.1038/s41598-021-89461-4.
@article{osti_1833737,
title = {QUBO formulations for training machine learning models},
author = {Date, Prasanna and Arthur, Davis and Pusey-Nazzaro, Lauren},
abstractNote = {Abstract Training machine learning models on classical computers is usually a time and compute intensive process. With Moore’s law nearing its inevitable end and an 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 can approximately solve NP-hard 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 problems on adiabatic quantum computers, they must be formulated as QUBO problems, which is very challenging. In this paper, we formulate the training problems of three machine learning models—linear regression, support vector machine (SVM) and balanced k-means clustering—as QUBO problems, making them conducive to be trained on adiabatic quantum computers. We also analyze the computational complexities of our formulations and compare them to corresponding state-of-the-art classical approaches. We show that the time and space complexities of our formulations are better (in case of SVM and balanced k-means clustering) or equivalent (in case of linear regression) to their classical counterparts.},
doi = {10.1038/s41598-021-89461-4},
journal = {Scientific Reports},
number = 1,
volume = 11,
place = {United Kingdom},
year = {Tue May 11 00:00:00 EDT 2021},
month = {Tue May 11 00:00:00 EDT 2021}
}
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