An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization

Wu, Zeguan; Mohammadisiahroudi, Mohammadhossein; Augustino, Brandon; Yang, Xiu; Terlaky, Tamás

doi:10.3390/e25020330

Open AccessArticle

An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization

by

Zeguan Wu

,

Mohammadhossein Mohammadisiahroudi

,

Brandon Augustino

,

Xiu Yang

and

Tamás Terlaky

^*

Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA 18015, USA

^*

Author to whom correspondence should be addressed.

Entropy 2023, 25(2), 330; https://doi.org/10.3390/e25020330

Submission received: 31 December 2022 / Revised: 7 February 2023 / Accepted: 8 February 2023 / Published: 10 February 2023

(This article belongs to the Special Issue Quantum Machine Learning 2022)

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Abstract

Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior point methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization problems. IPMs solve a Newton linear system at each iteration to compute the search direction; thus, QLSAs can potentially speed up IPMs. Due to the noise in contemporary quantum computers, quantum-assisted IPMs (QIPMs) only admit an inexact solution to the Newton linear system. Typically, an inexact search direction leads to an infeasible solution, so, to overcome this, we propose an inexact-feasible QIPM (IF-QIPM) for solving linearly constrained quadratic optimization problems. We also apply the algorithm to

ℓ_{1}

-norm soft margin support vector machine (SVM) problems, and demonstrate that our algorithm enjoys a speedup in the dimension over existing approaches. This complexity bound is better than any existing classical or quantum algorithm that produces a classical solution.

Keywords: quantum computing; interior point method; quadratic optimization

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MDPI and ACS Style

Wu, Z.; Mohammadisiahroudi, M.; Augustino, B.; Yang, X.; Terlaky, T. An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization. Entropy 2023, 25, 330. https://doi.org/10.3390/e25020330

AMA Style

Wu Z, Mohammadisiahroudi M, Augustino B, Yang X, Terlaky T. An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization. Entropy. 2023; 25(2):330. https://doi.org/10.3390/e25020330

Chicago/Turabian Style

Wu, Zeguan, Mohammadhossein Mohammadisiahroudi, Brandon Augustino, Xiu Yang, and Tamás Terlaky. 2023. "An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization" Entropy 25, no. 2: 330. https://doi.org/10.3390/e25020330

APA Style

Wu, Z., Mohammadisiahroudi, M., Augustino, B., Yang, X., & Terlaky, T. (2023). An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization. Entropy, 25(2), 330. https://doi.org/10.3390/e25020330

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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An Inexact Feasible Quantum Interior Point Method for Linearly Constrained Quadratic Optimization

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