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Nonlinear differential equations model diverse phenomena but are notoriously difficult to solve. While there has been extensive previous work on efficient quantum algorithms for linear differential equations, the linearity of quantum…

Partial differential equation solvers are required to solve the Navier-Stokes equations for fluid flow. Recently, algorithms have been proposed to simulate fluid dynamics on quantum computers. Fault-tolerant quantum devices might enable…

Fluid Dynamics · Physics 2025-05-20 Zhixin Song , Robert Deaton , Bryan Gard , Spencer H. Bryngelson

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

We propose a quantum algorithm for the linear advection-diffusion equation (ADE) Lattice-Boltzmann method (LBM) that leverages dynamic circuits. Dynamic quantum circuits allow for an optimized collision-operator quantum algorithm,…

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…

We present a method to split quantum circuits of variational quantum algorithms (VQAs) to allow for parallel training and execution, that maximally exploits the limited number of qubits in hardware to solve large problem instances. We apply…

Quantum Physics · Physics 2023-04-07 Michele Cattelan , Sheir Yarkoni

Quantum annealing is an emerging metaheuristic used for solving combinatorial optimisation problems. However, hardware based physical quantum annealers are primarily limited to a single vendor. As an alternative, we can discretise the…

Quantum Physics · Physics 2023-07-20 Ameya Bhave , Ajinkya Borle

Variational quantum algorithms (VQAs) have attracted remarkable interest over the past few years because of their potential computational advantages on near-term quantum devices. They leverage a hybrid approach that integrates classical and…

We simulate the nonlinear chaotic dynamics of Lorenz-type models for a classical two-dimensional thermal convection flow with 3 and 8 degrees of freedom by a hybrid quantum--classical reservoir computing model. The high-dimensional quantum…

Quantum Physics · Physics 2023-11-14 Philipp Pfeffer , Florian Heyder , Jörg Schumacher

We investigate the possibility and current limitations of flow computations using quantum annealers by solving a fundamental flow problem on Ising machines. As a fundamental problem, we consider the one-dimensional advection-diffusion…

Fluid Dynamics · Physics 2025-07-02 Kenichiro Takagi , Naoki Moriya , Shiori Aoki , Katsuhiro Endo , Mayu Muramatsu , Koji Fukagata

This paper develops a distributed variational quantum algorithm for solving large-scale linear equations. For a linear system of the form $Ax=b$, the large square matrix $A$ is partitioned into smaller square block submatrices, each of…

Quantum Physics · Physics 2026-04-03 Tong Shen , Zeru Zhu , Ji Liu

Quantum Support Vector Machines (QSVM) play a vital role in using quantum resources for supervised machine learning tasks, such as classification. However, current methods are strongly limited in terms of scalability on Noisy Intermediate…

Quantum Physics · Physics 2023-09-15 Jianming Yi , Kalyani Suresh , Ali Moghiseh , Norbert Wehn

We analyze the performance of the Harrow-Hassidim-Lloyd algorithm (HHL algorithm) for solving linear problems and of a variant of this algorithm (HHL variant) commonly encountered in literature. This variant relieves the algorithm of…

Quantum Physics · Physics 2024-10-25 Matias Ginzburg , Ugo Marzolino

State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…

We present an end-to-end quantum algorithm for simulating nonlinear dynamics described by a system of stochastic dissipative differential equations with a quadratic nonlinearity. The stochastic part of the system is modeled by a Gaussian…

Quantum Physics · Physics 2025-10-07 Sergey Bravyi , Robert Manson-Sawko , Mykhaylo Zayats , Sergiy Zhuk

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as…

Quantum Physics · Physics 2026-04-17 Austin Pechan , John Golden , Daniel O'Malley

Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. However, due to the noise and the limited scale of current quantum…

Quantum Physics · Physics 2024-03-05 Julien Gacon

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading…

Machine Learning · Computer Science 2022-06-16 Sami Khairy , Ruslan Shaydulin , Lukasz Cincio , Yuri Alexeev , Prasanna Balaprakash

We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…

Modern Cloud/Edge architectures need to orchestrate multiple layers of heterogeneous computing nodes, including pervasive sensors/actuators, distributed Edge/Fog nodes, centralized data centers and quantum devices. The optimal assignment…

Quantum Physics · Physics 2024-05-27 Carlo Mastroianni , Francesco Plastina , Jacopo Settino , Andrea Vinci