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The solution of large systems of nonlinear differential equations is needed for many applications in science and engineering. In this study, we present three main improvements to existing quantum algorithms based on the Carleman…

Quantum Physics · Physics 2025-08-21 Pedro C. S. Costa , Philipp Schleich , Mauro E. S. Morales , Dominic W. Berry

We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE…

Quantum Physics · Physics 2024-12-31 Soichiro Yamazaki , Fumio Uchida , Kotaro Fujisawa , Koichi Miyamoto , Naoki Yoshida

The Lattice Boltzmann Method (LBM) is widely recognized as an efficient algorithm for simulating fluid flows in both single-phase and multi-phase scenarios. In this research, a quantum Carleman Linearization formulation of the Lattice…

Quantum Physics · Physics 2024-03-05 Bastien Bakker , Thomas W. Watts

We apply Carleman linearization of the Lattice Boltzmann (CLB) representation of fluid flows to quantum emulate the dynamics of a 2D Kolmogorov-like flow. We assess the accuracy of the result and find a relative error of the order of…

Quantum Physics · Physics 2025-05-27 Claudio Sanavio , William A. Simon , Alexis Ralli , Peter Love , Sauro Succi

We present a quantum computing algorithm for fluid flows based on the Carleman-linearization of the Lattice Boltzmann (LB) method. First, we demonstrate the convergence of the classical Carleman procedure at moderate Reynolds numbers,…

Quantum Physics · Physics 2024-05-21 Claudio Sanavio , Sauro Succi

Quantum computing holds great promise to accelerate scientific computations in fluid dynamics and other classical physical systems. While various quantum algorithms have been proposed for linear flows, developing quantum algorithms for…

Fluid Dynamics · Physics 2025-02-25 Boyuan Wang , Zhaoyuan Meng , Yaomin Zhao , Yue Yang

It is proposed a dimensional Lattice Boltzmann Method (LBM) of wide application for simulating fluid flow and heat transfer problems. The proposed LBM consists in the numerical solution of the discrete lattice Boltzmann equation (LBE) using…

Fluid Dynamics · Physics 2024-05-14 Ivan Talão Martins , Pablo Fariñas Alvariño , Luben Cabezas-Gómez

In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…

Quantum Physics · Physics 2025-02-03 Hsuan-Cheng Wu , Jingyao Wang , Xiantao Li

We propose a quantum algorithm for solving physical problems represented by the lattice Boltzmann formulation. Specifically, we deal with the case of a single phase, incompressible fluid obeying the Bhatnagar-Gross-Krook model. We use the…

Quantum Physics · Physics 2023-04-13 Wael Itani , Katepalli R. Sreenivasan , Sauro Succi

This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass…

We consider different Linear Combination of Unitaries (LCU) decompositions for molecular electronic structure Hamiltonians. Using these LCU decompositions for Hamiltonian simulation on a quantum computer, the main figure of merit is the…

Quantum Physics · Physics 2023-06-13 Ignacio Loaiza , Alireza Marefat Khah , Nathan Wiebe , Artur F. Izmaylov

We review the recent progress on studying the nuclear collective dynamics by solving the Boltzmann-Uehling-Uhlenbeck (BUU) equation with the lattice Hamiltonian method treating the collision term by the full-ensemble stochastic collision…

Nuclear Theory · Physics 2020-10-16 Rui Wang , Zhen Zhang , Lie-Wen Chen , Yu-Gang Ma

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,…

The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a…

Quantum Physics · Physics 2025-10-20 Ivan Novikau , Ilon Joseph

We provide novel linear combination of unitaries decompositions for a class of discrete elliptic differential operators. Specifically, Poisson problems augmented with periodic, Dirichlet, Neumann, Robin, and mixed boundary conditions are…

Quantum Physics · Physics 2026-01-13 Thomas Hogancamp , Reuben Demirdjian , Daniel Gunlycke

We propose a simple method for simulating a general class of non-unitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem, or on…

Quantum Physics · Physics 2023-10-24 Dong An , Jin-Peng Liu , Lin Lin

The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While the LBM is highly parallelizable on classical hardware, its…

Quantum Physics · Physics 2026-04-14 Trong Duong , Matthias Möller , Norbert Hosters

With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM) mimics a second order Crank-Nicolson scheme for certain types of balance laws (Farag et al. [2021]). This allows the explicit, highly parallelisable LBM to…

Computational Engineering, Finance, and Science · Computer Science 2023-07-27 Erik Faust , Alexander Schlüter , Henning Müller , Ralf Müller

The quantum Lattice Boltzmann equation (QLBe), a new variant of the lattice Boltzmann equation, specifically designed to describe non relativistic quantum motion, is validated for the case of a free-particle in (1+1) space-time dimensions.…

comp-gas · Physics 2008-02-03 S. Succi