Efficient Use of Quantum Linear System Algorithms in Inexact Infeasible IPMs for Linear Optimization

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially quantum interior point methods (QIPMs), to...

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Vydáno v:Journal of optimization theory and applications Ročník 202; číslo 1; s. 146 - 183
Hlavní autoři: Mohammadisiahroudi, Mohammadhossein, Fakhimi, Ramin, Terlaky, Tamás
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.07.2024
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Conjugate gradient method
Engineering
Error analysis
Exact solutions
Linear systems
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quantum computing
Simulators
Solvers
Theory of Computation
Quantum linear system algorithm
90C51
Quantum interior point method
81P68
Iterative refinement
90C05
Linear optimization
ISSN:0022-3239, 1573-2878
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Shrnutí:Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially quantum interior point methods (QIPMs), to solve convex conic 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 in detail the use of quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point (II-QIPM) is developed to solve linear optimization problems. We also discuss how we can get an exact solution by iterative refinement (IR) without excessive time of quantum solvers. The proposed IR-II-QIPM shows exponential speed-up with respect to precision compared to previous II-QIPMs. Additionally, we present a quantum-inspired classical variant of the proposed IR-II-QIPM where QLSAs are replaced by conjugate gradient methods. This classic IR-II-IPM has some advantages compared to its quantum counterpart, as well as previous classic inexact infeasible IPMs. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are presented and analyzed.
Bibliografie:ObjectType-Article-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02452-z