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quantum linear system algorithm applied to communication systems

quantum INFORMATION PROCESSING 2022年第7期21卷 1-15页

作者： Park, Jeonghoon Heo, Jun Korea Univ Res Inst Informat & Commun Technol Seoul 02841 South Korea Korea Univ Sch Elect Engn Seoul 02841 South Korea

A quantum linear system algorithm (QLSA) can solve linear equations more efficiently than classical ones. However, we cannot know the value of each component of a solution directly because a QLSA produces a solution as a quantum state. In this paper, we present a method to obtain classical information of a solution with the exponential quantum advantage of a QLSA when the values of a solution are on a rectangular grid in the complex plane. Our method can extract both the amplitude and phase information by modifying the given matrix. Moreover, we show an application to a specific problem in communication systems.

关键词： quantum linear system algorithm Read-out problem MIMO detection

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Applications of a quantum linear system algorithm to linear MIMO Detections

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IEEE ACCESS 2022年 10卷 36233-36245页

作者： Park, Jeonghoon Seo, Youngjin Heo, Jun Korea Univ Res Inst Informat & Commun Technol Seoul 02841 South Korea Korea Univ Sch Elect Engn Seoul 02841 South Korea

A linear system can be solved more efficiently by quantum computing. However, previously known quantum algorithms provide only a quantum state as the solution;consequently, we cannot obtain the value of each component of the solution. We propose a method to extract the component values of the solution, and we present an application to linear multiple-input multiple-output (MIMO) detections. In the proposed algorithm, we demonstrate a concrete method that applies a quantum linear system algorithm (QLSA) when the components of a solution have binary variables, quaternary variables, or roots of a complex number. Whereas the conventional method requires an additional process to read out the values of the components, the proposed algorithm does not need any post-procedure. Instead, our method uses a QLSA iteratively, and the number of uses is logarithmic in the size of the linear system. Thus, our method maintains the runtime with the quantum advantage, but the conventional approach increases the runtime significantly. Furthermore, the application of the proposed method shows that quantum computing can collaborate with communication systems for large-scale MIMO systems.

关键词： quantum state quantum computing MIMO communication Logic gates linear systems Qubit Runtime linear MIMO detection quantum computing quantum linear system algorithm

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Efficient Use of quantum linear system algorithms in Inexact Infeasible IPMs for linear Optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第1期202卷 146-183页

作者： Mohammadisiahroudi, Mohammadhossein Fakhimi, Ramin Terlaky, Tamas Lehigh Univ Bethlehem PA 18015 USA

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.

关键词： quantum interior point method linear optimization quantum linear system algorithm Iterative refinement

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Estimating QSVT angles for matrix inversion with large condition numbers

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JOURNAL OF COMPUTATIONAL PHYSICS 2025年 525卷

作者： Novikau, I. Joseph, I. Lawrence Livermore Natl Lab 7000 East Ave Livermore CA 94550 USA

quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. We propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems.

关键词： quantum computing QSVT Matrix inversion quantum linear system algorithm

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Improvements to quantum Interior Point Method for linear Optimization

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ACM TRANSACTIONS ON quantum COMPUTING 2025年第1期6卷 1-24页

作者： Mohammadisiahroudi, Mohammadhossein Wu, Zeguan Augustino, Brandon Carr, Arielle Terlaky, Tamas Lehigh Univ Ind & Syst Engn Dept Bethlehem PA 18015 USA MIT Sloan Sch Management Cambridge MA USA Lehigh Univ Comp Sci & Engn Dept Bethlehem PA USA

quantum linear system algorithms (QLSAs) have the potential to speed up Interior Point Methods (IPMs). However, a major bottleneck is the inexactness of quantum tomography to extract classical solutions from quantum states. In addition, QLSAs are sensitive to the condition number, and this sensitivity is exacerbated when the Newton systems arising in IPMs converge to a singular matrix. Recently, an Inexact Feasible quantum IPM (IF-QIPM) has been developed that addresses the inexactness of QLSAs. However, this method requires a large number of gates and qubits to be implemented. Here, we propose a new IF-QIPM using the normal equation system, which requires fewer gates and qubits. To mitigate the sensitivity to the condition number and other input data-related parameters, we use preconditioning coupled with iterative refinement to obtain better complexity. Finally, we demonstrate the effectiveness of our approach on IBM Qiskit simulators.

关键词： quantum linear system algorithm quantum interior point method linear optimization iterative refinement preconditioning

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MMSE detection method in uplink massive MIMO systems based on quantum computing

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PHYSICS LETTERS A 2019年第12期383卷 1268-1273页

作者： Wang, XiaoJun Zhao, Jie Meng, FanXu Yu, XuTao Zhang, ZaiChen Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Jiangsu Peoples R China Southeast Univ State Key Lab Millimeter Waves Nanjing 210096 Jiangsu Peoples R China

The minimum mean square error (MMSE) detection method involved matrix inversion operation with excessive computational burden. In this paper, we develop an improved quantum linear system algorithm to solve matrix inversion problem of the MMSE detection method in uplink massive multiple-input and multiple-output (MIMO) systems. In order to apply reasonably the robust computational power of quantum computing, we optimize the preparation of the input state and the extraction of the solution from the final entangled quantum state. We prove that this algorithm can reduce computational complexity to O (N log N). (C) 2019 Elsevier B.V. All rights reserved.

关键词： Uplink massive MIMO systems quantum computing MMSE detection quantum linear system algorithm

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quantum-enhanced Regression Analysis Using State-of-the-art QLSAs and QIPMs 7

Quantum-enhanced Regression Analysis Using State-of-the-art ...

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IEEE/ACM 7th Symposium on Edge Computing (SEC)

作者： Mohammadisiahroudi, Mohammadhossein Wu, Zeguan Augustino, Brandon Terlaky, Tamas Carr, Arielle Lehigh Univ Ind & Syst Engn Dept Bethlehem PA 18015 USA Lehigh Univ Comp Sci & Engn Dept Bethlehem PA 18015 USA

ISBN: (纸本)9781665486118

quantum computing has the potential to speed up machine learning methods. One major direction is using quantum linear algebra to solve linear system problems or optimization problems in the machine learning area. quantum approaches in the literature for different types of least squares problems demonstrate speedups w.r.t. dimension but have disadvantages w.r.t. precision and condition number. In this paper, we discuss how an iterative refinement scheme can deliver an accurate solution without the excessive cost of quantum linear system algorithms (QLSAs). In addition, we propose an adaptive regularization approach that can mitigate the effect of condition number on solution time. In the second part of this paper, we investigate how state-of-the-art quantum Interior Point Methods (QIPMs) can solve more sophisticated regression problems such as Lasso regression and support vector machine problems, which can be reformulated as quadratic optimization problems.

关键词： quantum Machine Learning quantum Interior Point Method quantum linear system algorithm Least Squares Method Support Vector Machine Lasso Regression Iterative Refinement

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