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The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the…

Quantum Physics · Physics 2022-09-23 Walter Robson , Kamal K. Saha , Connor Howington , In-Saeng Suh , Jaroslaw Nabrzyski

In the future high-luminosity LHC era, high-energy physics experiments face unprecedented computational challenges for event reconstruction. Employing the LHCb vertex locator as a case study we investigate a novel approach for charged…

Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…

Quantum Physics · Physics 2014-02-21 Dominic W. Berry

Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…

Superconducting quantum circuits are promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm…

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

High-energy physics is facing increasingly computational challenges in real-time event reconstruction for the near-future high-luminosity era. Using the LHCb vertex detector as a use-case, we explore a new algorithm for particle track…

Under the nearing error-corrected era of quantum computing, it is necessary to understand the suitability of certain post-NISQ algorithms for practical problems. One of the most promising, applicable and yet difficult to implement in…

Quantum Physics · Physics 2025-05-29 Mark Danza , Sonia Lopez Alarcon , Cory Merkel

A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…

Quantum Physics · Physics 2023-11-10 Nhat A. Nghiem , Tzu-Chieh Wei

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

The Harrow, Hassidim, Lloyd (HHL) algorithm is a quantum algorithm expected to accelerate solving large-scale linear ordinary differential equations (ODEs). To apply the HHL to non-linear problems such as chemical reactions, the system must…

Numerical Analysis · Mathematics 2022-07-06 Takaki Akiba , Youhi Morii , Kaoru Maruta

Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…

Quantum Physics · Physics 2014-02-19 Jian Pan , Yudong Cao , Xiwei Yao , Zhaokai Li , Chenyong Ju , Xinhua Peng , Sabre Kais , Jiangfeng Du

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

This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…

Quantum Physics · Physics 2024-12-10 Sajad Fathi Hafshejani , Md Mohsin Uddin , David Neufeld , Daya Gaur , Robert Benkoczi

The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…

Quantum Physics · Physics 2022-06-14 Fang Gao , Guojian Wu , Mingyu Yang , Wei Cui , Feng Shuang

Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…

Quantum Physics · Physics 2021-12-14 John M. Martyn , Zane M. Rossi , Andrew K. Tan , Isaac L. Chuang

Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the…

Quantum Physics · Physics 2019-01-10 Kosuke Mitarai , Masahiro Kitagawa , Keisuke Fujii

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

Power flow calculation plays an important role in planning, operation, and control of the power system. The quantum HHL algorithm can achieve theoretical exponential speedup over classical algorithms on DC power flow calculation. Since the…

Quantum Physics · Physics 2022-06-09 Fang Gao , Guojian Wu , Suhang Guo , Wei Dai , Feng Shuang

The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps…

Quantum Physics · Physics 2023-07-06 Ana Martin , Ruben Ibarrondo , Mikel Sanz