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Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…

Quantum Physics · Physics 2025-02-20 Nhat A. Nghiem

Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…

Quantum Physics · Physics 2024-10-04 Hakikat Singh

Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…

Quantum Physics · Physics 2025-10-16 Siddharth Hariprakash , Roel Van Beeumen , Katherine Klymko , Daan Camps

Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…

Quantum Physics · Physics 2017-12-27 Andrew M. Childs , Robin Kothari , Rolando D. Somma

HHL algorithm \cite{harrow} to solve linear system is a powerful and efficient quantum technique to deal with many matrix operations (such as matrix multiplication, powers and inversion). It inspires many applications in quantum machine…

Quantum Physics · Physics 2018-08-17 Changpeng Shao

Variational Quantum Algorithms (VQAs) have emerged as promising methods for tackling complex problems on near-term quantum devices. Among these algorithms, the Variational Quantum Linear Solver (VQLS) addresses linear systems of the form…

Quantum Physics · Physics 2024-09-11 Gloria Turati , Alessia Marruzzo , Maurizio Ferrari Dacrema , Paolo Cremonesi

Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavour. We prove that…

Quantum Physics · Physics 2024-07-25 Pradeep Kumar , Tanoy Kanti Konar , Leela Ganesh Chandra Lakkaraju , Aditi Sen De

Following the celebrated quantum algorithm for solving linear equations (so-called HHL algorithm), Childs, Kothari and Somma [SIAM Journal on Computing, {\bf 46}: 1920, (2017)] provided an approach to solve a linear system of equations with…

Quantum Physics · Physics 2023-12-06 Nhat A. Nghiem , Tzu-Chieh Wei

Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…

Quantum Physics · Physics 2026-03-10 Francesco Ghisoni , Francesco Scala , Daniele Bajoni , Dario Gerace

Multiple linear regression assumes an imperative role in supervised machine learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed that their HHL algorithm can be used to sample the solution of a linear system…

The Harrow-Hassidim-Lloyd (HHL) algorithm offers exponential speedup for solving the quantum linear-system problem. But some caveats for the speedup could be hard to met. One of the difficulties is the encoding bottleneck, i.e., the…

Quantum Physics · Physics 2025-03-11 Guang Ping He

Quantum computation offers a promising alternative to classical computing methods in many areas of numerical science, with algorithms that make use of the unique way in which quantum computers store and manipulate data often achieving…

Quantum Physics · Physics 2022-07-19 Christopher D. Phillips , Vladimir I. Okhmatovski

Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…

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…

Quantum Physics · Physics 2023-02-14 Mohammadhossein Mohammadisiahroudi , Ramin Fakhimi , Tamás Terlaky

Solving linear systems of equations is an important problem in science and engineering. Many quantum algorithms, such as the Harrow-Hassidim-Lloyd (HHL) algorithm (for quantum-gate computers) and the box algorithm (for quantum-annealing…

Computational Engineering, Finance, and Science · Computer Science 2024-05-07 Sanjay Suresh , Krishnan Suresh

We propose a novel quantum algorithm for solving nuclear resonances, which is based on the iterative Harrow-Hassidim-Lloyd algorithm and eigenvector continuation with complex scaling. To validate this approach, we compute the resonant…

Quantum Physics · Physics 2025-06-27 Hantao Zhang , Dong Bai , Zhongzhou Ren

This letter is a proof of concept for quantum power flow (QPF) algorithms which underpin various unprecedentedly efficient power system analytics exploiting quantum computing. Our contributions are three-fold: 1) Establish a…

Quantum Physics · Physics 2021-04-13 Fei Feng , Yifan Zhou , Peng Zhang

This is a series of studies devoted to modeling and solving heat and mass transfer problems occurring in electric contacts where we employ and develop mathematical apparatus along with quantum algorithms for solving moving boundary value…

Computational Physics · Physics 2020-10-13 Merey M. Sarsengeldin , Zuhair M. Nashed

Different hybrid quantum-classical algorithms have recently been developed as a near-term way to solve linear systems of equations on quantum devices. However, the focus has so far been mostly on the methods, rather than the problems that…

Computational Engineering, Finance, and Science · Computer Science 2024-12-09 Giorgio Tosti Balducci , Boyang Chen , Matthias Möller , Roeland De Breuker

Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…