Version 1
: Received: 2 March 2023 / Approved: 3 March 2023 / Online: 3 March 2023 (04:06:57 CET)
How to cite:
Mohammadisiahroudi, M.; Fakhimi, R.; Terlaky, T. Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization. Preprints2023, 2023030056. https://doi.org/10.20944/preprints202303.0056.v1
Mohammadisiahroudi, M.; Fakhimi, R.; Terlaky, T. Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization. Preprints 2023, 2023030056. https://doi.org/10.20944/preprints202303.0056.v1
Mohammadisiahroudi, M.; Fakhimi, R.; Terlaky, T. Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization. Preprints2023, 2023030056. https://doi.org/10.20944/preprints202303.0056.v1
APA Style
Mohammadisiahroudi, M., Fakhimi, R., & Terlaky, T. (2023). Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization. Preprints. https://doi.org/10.20944/preprints202303.0056.v1
Chicago/Turabian Style
Mohammadisiahroudi, M., Ramin Fakhimi and Tamás Terlaky. 2023 "Efficient Use of Quantum Linear System Algorithms in Interior Point Methods for Linear Optimization" Preprints. https://doi.org/10.20944/preprints202303.0056.v1
Abstract
Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventionalsupercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.
Keywords
Quantum Interior Point Method; Linear Optimization; Quantum Linear System Algorithm; Iterative Refinement
Subject
Computer Science and Mathematics, Data Structures, Algorithms and Complexity
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
