Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Access

Applications of a Quantum Linear System Algorithm to Linear MIMO Detections

Jeonghoon Park, Youngjin Seo, Jun Heo

Published Jan 1, 2022• 5 citations
Publisher

Abstract

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.

DOI
10.1109/access.2022.3164071

Related papers

Quantum Computing-Assisted Channel Estimation for Massive MIMO mmWave Systems

Evangelos Vlachos, Kostas Blekos

Quantum computing (QC)-assisted algorithms promise exponential increase in the computational efficiency, enabling instant solution of large systems of equations. Massive multiple-input multiple-output (MIMO) millimeter-wave (mmWave) systems pose extraordinary demands in computational complexity, due to the usage of huge antenna arrays, massive number of users, and ultra low-latency requirements. This work provides an initial discussion on how QC-based algorithms for solving linear systems of equations could be utilized for assisting the basic operations of the transceivers physical-layer, such as the channel estimation. We identify the connections between the amplitude encoding in the quantum domain and the recovery of the channel information.

IFIP/IEEE International Conference on Very Large Scale Integration•Oct 3, 2022•7 citations

Hybrid Quantum-Classical Approaches to Optimize Signal Processing in Massive MIMO Arrays

Shaik Anjimoon, Baswaraju Swathi, Rajeev Sobti +3 more

This paper introduces a pioneering method in the realm of signal processing for Massive Multiple-Input Multiple-Output (MIMO) systems, leveraging the synergistic potential of hybrid quantum-classical computing paradigms. The escalating demand for high data rate communications necessitates the advancement of MIMO technologies. However, the computational complexity associated with signal processing in such systems, especially in scenarios involving large array sizes, presents a significant challenge. This study proposes an innovative framework that integrates quantum computing algorithms with traditional classical methods to address this challenge. The quantum algorithms are specifically designed to expedite matrix operations and optimization tasks that are central to MIMO signal processing, such as channel estimation and precoding. A comparative analysis with purely classical approaches demonstrates a substantial improvement in computational efficiency and latency reduction, while maintaining, and in certain aspects enhancing, the accuracy of signal detection and system throughput. Furthermore, this hybrid approach offers scalability and adaptability to varying channel conditions and system configurations, a crucial feature for next-generation wireless communication systems. The theoretical foundation is complemented by simulation results, showcasing the feasibility and effectiveness of this approach in practical scenarios. This research not only paves the way for advanced signal processing techniques in Massive MIMO systems but also opens new horizons in the application of quantum computing in telecommunications.

International Conference on Communication, Computer Sciences and Engineering (IC3SE)•May 9, 2024•4 citations

A Quantum Dual Logarithmic Barrier Method for Linear Optimization

Zeguan Wu, Pouya Sampourmahani, Mohammadhossein Mohammadisiahroudi +1 more

Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via quantum linear system algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require solving linear systems, such as the dual logarithmic barrier method (DLBM) for solving linear optimization (LO) problems. In this paper, we use a QLSA to solve the linear systems arising in each iteration of the DLBM. To use the QLSA in a hybrid setting, we read out quantum states via a tomography procedure that introduces considerable error and noise. Thus, this paper first proposes an inexact feasible variant of DLBM for LO problems and then extends it to a quantum version. Our quantum approach has quadratic convergence toward the central path with inexact directions, and we show that this method has the best known [Formula: see text] iteration complexity, where n is the number of variables, [Formula: see text] is the initial duality gap, and [Formula: see text] is the accuracy. We further use iterative refinement to improve the complexity dependence on accuracy and condition number. For LO problems with quadratically more constraints than variables, the quantum complexity of our method has a sublinear dependence on dimension. Funding: This research was supported by Defense Advanced Research Projects Agency [Grant W911NF2010022] and the National Science Foundation [Grant 2128527].

arXiv:2412.15977•INFORMS Journal on Optimization•Dec 5, 2025•1 citation

Quantum Multigrid Algorithm for Finite Element Problems

Osama M. Raisuddin, Suvranu De

Quantum linear system algorithms (QLSAs) can provide exponential speedups for the solution of linear systems, but the growth of the condition number for finite element problems can eliminate the exponential speedup. QLSAs are also incapable of using an initial guess of a solution to improve upon it. To circumvent these issues, we present a Quantum Multigrid Algorithm (qMG) for the iterative solution of linear systems by applying the sequence of multigrid operations on a quantum state. Given an initial guess with error e_0, qMG can produce a vector encoding the entire sequence of multigrid iterates with the final iterate having a relative error e'=e/e_0, as a subspace of the final quantum state, with exponential advantage in O( poly log (N/e') ) time using O( poly log (N/e') ) qubits. Although extracting the final iterate from the sequence is efficient, extracting the sequence of iterates from the final quantum state can be inefficient. We provide an analysis of the complexity of the method along with numerical analysis.

arXiv:2404.07466•Apr 11, 2024•4 citations

An analysis of iterative refinement for quantum linear system solvers

Adrian Harkness, Mohammadhossein Mohammadisiahroudi, Brandon Augustino +2 more

We present and analyze an iterative refinement (IR) framework for improving the precision dependence of algorithms that combine a quantum linear system algorithm (QLSA) with quantum state tomography. Existing QLSAs achieve polylogarithmic dependence on the inverse error tolerance to prepare a quantum state encoding the solution, but extracting a classical description of such a state via tomography typically introduces a polynomial dependence on the target precision. To retain polylogarithmic dependence in the inverse error tolerance throughout the entire process, we develop an IR scheme that solves a sequence of related linear systems to progressively refine the solution while requiring only fixed-precision quantum subroutines, finally obtaining a classical description of a high-precision solution. We analyze the proposed framework under three input models: quantum-read/classical-write RAM (QRAM), linear combinations of unitaries (LCU), and sparse-access oracles. We evaluate the proposed scheme through numerical experiments on both quantum simulators and real quantum hardware. The results demonstrate that iterative refinement efficiently improves the precision of the solution and exhibits robustness to hardware noise.

quant-pharXiv:2609.10250•Sep 10, 2026•0 citations

An Efficient Quantum Algorithm for Linear System Problem in Tensor Format

Zeguan Wu, Sidhant Misra, Tamás Terlaky B +2 more

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of the problem dimension. However, low-complexity circuit implementations of the oracles assumed in these QLSAs constitute the major bottleneck for practical quantum speed-up in solving linear systems. In this work, we focus on the application of QLSAs for linear systems that are expressed as a low rank tensor sums, which arise in solving discretized PDEs. Previous works uses modified Krylov subspace methods to solve such linear systems with a per-iteration complexity being polylogarithmic of the dimension but with no guarantees on the total convergence cost. We propose a quantum algorithm based on the recent advances on adiabatic-inspired QLSA and perform a detailed analysis of the circuit depth of its implementation. We rigorously show that the total complexity of our implementation is polylogarithmic in the dimension, which is comparable to the per-iteration complexity of the classical heuristic methods.

arXiv:2403.19829•Mar 28, 2024•0 citations
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.
Quantum computing (QC)-assisted algorithms promise exponential increase in the computational efficiency, enabling instant solution of large systems of equations. Massive multiple-input multiple-output (MIMO) millimeter-wave (mmWave) systems pose extraordinary demands in computational complexity, due to the usage of huge antenna arrays, massive number of users, and ultra low-latency requirements. This work provides an initial discussion on how QC-based algorithms for solving linear systems of equations could be utilized for assisting the basic operations of the transceivers physical-layer, such as the channel estimation. We identify the connections between the amplitude encoding in the quantum domain and the recovery of the channel information.
This paper introduces a pioneering method in the realm of signal processing for Massive Multiple-Input Multiple-Output (MIMO) systems, leveraging the synergistic potential of hybrid quantum-classical computing paradigms. The escalating demand for high data rate communications necessitates the advancement of MIMO technologies. However, the computational complexity associated with signal processing in such systems, especially in scenarios involving large array sizes, presents a significant challenge. This study proposes an innovative framework that integrates quantum computing algorithms with traditional classical methods to address this challenge. The quantum algorithms are specifically designed to expedite matrix operations and optimization tasks that are central to MIMO signal processing, such as channel estimation and precoding. A comparative analysis with purely classical approaches demonstrates a substantial improvement in computational efficiency and latency reduction, while maintaining, and in certain aspects enhancing, the accuracy of signal detection and system throughput. Furthermore, this hybrid approach offers scalability and adaptability to varying channel conditions and system configurations, a crucial feature for next-generation wireless communication systems. The theoretical foundation is complemented by simulation results, showcasing the feasibility and effectiveness of this approach in practical scenarios. This research not only paves the way for advanced signal processing techniques in Massive MIMO systems but also opens new horizons in the application of quantum computing in telecommunications.
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via quantum linear system algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require solving linear systems, such as the dual logarithmic barrier method (DLBM) for solving linear optimization (LO) problems. In this paper, we use a QLSA to solve the linear systems arising in each iteration of the DLBM. To use the QLSA in a hybrid setting, we read out quantum states via a tomography procedure that introduces considerable error and noise. Thus, this paper first proposes an inexact feasible variant of DLBM for LO problems and then extends it to a quantum version. Our quantum approach has quadratic convergence toward the central path with inexact directions, and we show that this method has the best known [Formula: see text] iteration complexity, where n is the number of variables, [Formula: see text] is the initial duality gap, and [Formula: see text] is the accuracy. We further use iterative refinement to improve the complexity dependence on accuracy and condition number. For LO problems with quadratically more constraints than variables, the quantum complexity of our method has a sublinear dependence on dimension. Funding: This research was supported by Defense Advanced Research Projects Agency [Grant W911NF2010022] and the National Science Foundation [Grant 2128527].
Quantum linear system algorithms (QLSAs) can provide exponential speedups for the solution of linear systems, but the growth of the condition number for finite element problems can eliminate the exponential speedup. QLSAs are also incapable of using an initial guess of a solution to improve upon it. To circumvent these issues, we present a Quantum Multigrid Algorithm (qMG) for the iterative solution of linear systems by applying the sequence of multigrid operations on a quantum state. Given an initial guess with error e_0, qMG can produce a vector encoding the entire sequence of multigrid iterates with the final iterate having a relative error e'=e/e_0, as a subspace of the final quantum state, with exponential advantage in O( poly log (N/e') ) time using O( poly log (N/e') ) qubits. Although extracting the final iterate from the sequence is efficient, extracting the sequence of iterates from the final quantum state can be inefficient. We provide an analysis of the complexity of the method along with numerical analysis.
We present and analyze an iterative refinement (IR) framework for improving the precision dependence of algorithms that combine a quantum linear system algorithm (QLSA) with quantum state tomography. Existing QLSAs achieve polylogarithmic dependence on the inverse error tolerance to prepare a quantum state encoding the solution, but extracting a classical description of such a state via tomography typically introduces a polynomial dependence on the target precision. To retain polylogarithmic dependence in the inverse error tolerance throughout the entire process, we develop an IR scheme that solves a sequence of related linear systems to progressively refine the solution while requiring only fixed-precision quantum subroutines, finally obtaining a classical description of a high-precision solution. We analyze the proposed framework under three input models: quantum-read/classical-write RAM (QRAM), linear combinations of unitaries (LCU), and sparse-access oracles. We evaluate the proposed scheme through numerical experiments on both quantum simulators and real quantum hardware. The results demonstrate that iterative refinement efficiently improves the precision of the solution and exhibits robustness to hardware noise.
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of the problem dimension. However, low-complexity circuit implementations of the oracles assumed in these QLSAs constitute the major bottleneck for practical quantum speed-up in solving linear systems. In this work, we focus on the application of QLSAs for linear systems that are expressed as a low rank tensor sums, which arise in solving discretized PDEs. Previous works uses modified Krylov subspace methods to solve such linear systems with a per-iteration complexity being polylogarithmic of the dimension but with no guarantees on the total convergence cost. We propose a quantum algorithm based on the recent advances on adiabatic-inspired QLSA and perform a detailed analysis of the circuit depth of its implementation. We rigorously show that the total complexity of our implementation is polylogarithmic in the dimension, which is comparable to the per-iteration complexity of the classical heuristic methods.