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Quantum algorithms with a proven theoretical speedup over classical computation are rare. Among the most prominent is the Harrow-Hassidim-Lloyd (HHL) algorithm for solving sparse linear systems. Here, HHL is applied to encode melodic…

Quantum Physics · Physics 2026-04-24 Alexis Kirke

With the advent and development of quantum computers, various quantum algorithms that can solve linear equations and eigenvalues faster than classical computers have been developed. The Harrow-Hassidim-Lloyd algorithm is an algorithm that…

Quantum Physics · Physics 2025-06-23 Hyunju Lee , Kyungtaek Jun

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

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

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

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

In this paper, we explore using the Harrow-Hassidim-Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing…

Quantum Physics · Physics 2025-08-08 Muqing Zheng , Chenxu Liu , Samuel Stein , Xiangyu Li , Johannes Mülmenstädt , Yousu Chen , Ang Li

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

Climate change is becoming one of the greatest challenges to the sustainable development of modern society. Renewable energies with low density greatly complicate the online optimization and control processes, where modern advanced…

Quantum Physics · Physics 2024-09-09 Junyu Liu , Han Zheng , Masanori Hanada , Kanav Setia , Dan Wu

Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an…

Quantum Physics · Physics 2023-07-20 Aidan Pellow-Jarman , Ilya Sinayskiy , Anban Pillay , Francesco Petruccione

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 present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher…

Quantum Physics · Physics 2024-11-12 Jack Morgan , Eric Ghysels , Hamed Mohammadbagherpoor

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…

With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all science and engineering. The Harrow-Hassidim-Lloyd algorithm, a…

Quantum Physics · Physics 2022-01-25 Kyungtaek Jun

Solving systems of linear equations is a key subroutine in many quantum algorithms. In the last 15 years, many quantum linear solvers (QLS) have been developed, competing to achieve the best asymptotic worst-case complexity. Most QLS assume…

Quantum algorithms for solving linear systems of equations have generated excitement because of the potential speed-ups involved and the importance of solving linear equations in many applications. However, applying these algorithms can be…

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

Though quantum algorithm acts as an important role in quantum computation science, not only for providing a great vision for solving classically unsolvable problems, but also due to the fact that it gives a potential way of understanding…

Quantum Physics · Physics 2015-08-11 Xiang Zhan , Jian Li , Hao Qin , Zhihao Bian , Peng Xue

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

The development of quantum processors capable of handling practical fluid flow problems represents a distant yet promising frontier. Recent strides in quantum algorithms, particularly linear solvers, have illuminated the path toward quantum…