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Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

Quantum Physics · Physics 2023-05-02 Shantanav Chakraborty , Aditya Morolia , Anurudh Peduri

We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…

Fluid Dynamics · Physics 2024-07-30 Zhen Lu , Yue Yang

Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be…

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 present a simplified exposition of some pieces of [Gily\'en, Su, Low, and Wiebe, STOC'19, arXiv:1806.01838], which introduced a quantum singular value transformation (QSVT) framework for applying polynomial functions to block-encoded…

Quantum Physics · Physics 2023-10-31 Ewin Tang , Kevin Tian

Quantum computing uses the physical principles of very small systems to develop computing platforms which can solve problems that are intractable on conventional supercomputers. There are challenges not only in building the required…

Quantum Physics · Physics 2024-11-19 Dieter Jaksch , Peyman Givi , Andrew J. Daley , Thomas Rung

The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…

Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…

Numerical Analysis · Mathematics 2026-04-22 Eky Febrianto , Yiren Wang , Burigede Liu , Michael Ortiz , Fehmi Cirak

Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, we first propose two quantum algorithms for solving quantum linear systems of equations with coherent…

Quantum Physics · Physics 2024-05-14 Qiqing Xia , Qianru Zhu , Huiqin Xie , Li Yang

Differentiable models of physical systems provide a powerful platform for gradient-based algorithms, with particular impact on parameter estimation and optimal control. Quantum systems present a particular challenge for such…

Quantum Physics · Physics 2025-09-09 David L. Craig , Natalia Ares , Erik M. Gauger

While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…

Quantum Physics · Physics 2025-12-29 Cheng Xue , Yu-Chun Wu , Guo-Ping Guo

The theory of quantum algorithms promises unprecedented benefits of harnessing the laws of quantum mechanics for solving certain computational problems. A persistent obstacle to using such algorithms for solving a wide range of real-world…

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…

Numerical Analysis · Mathematics 2026-04-28 Eunsik Choi , Jungin E. Kim , Xueling Lu , Yan Wang

Variational quantum algorithms have found success in the NISQ era owing to their hybrid quantum-classical approach which mitigate the problems of noise in quantum computers. In our study we introduce the dynamic ansatz in the Variational…

Quantum Physics · Physics 2022-02-08 Hrushikesh Patil , Yulun Wang , Predrag Krstic

Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…

Quantum Physics · Physics 2024-09-10 Yuki Sato , Ruho Kondo , Ikko Hamamura , Tamiya Onodera , Naoki Yamamoto

Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…

We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…

Quantum Physics · Physics 2015-05-30 Yudong Cao , Anmer Daskin , Steven Frankel , Sabre Kais

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator…

Quantum Physics · Physics 2026-04-17 Ivan Novikau , Ilon Joseph

Designing high-fidelity quantum circuits remains challenging, and current paradigms often depend on heuristic, fixed-ansatz structures or rule-based compilers that can be suboptimal or lack generality. We introduce a neuro-symbolic…

Quantum Physics · Physics 2026-04-10 Antonin Sulc