Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics

• URL: http://arxiv.org/abs/2502.16568v1
• Date: Sun, 23 Feb 2025 13:25:35 GMT
• Title: Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics
• Authors: Boyuan Wang, Zhaoyuan Meng, Yaomin Zhao, Yue Yang,
• Abstract summary: We introduce a novel ensemble description of lattice gas for simulating nonlinear fluid dynamics on a quantum computer.<n>We propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality.
• Score: 12.270811823319576
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 nonlinear problems remains a significant challenge. We introduce a novel node-level ensemble description of lattice gas for simulating nonlinear fluid dynamics on a quantum computer. This approach combines the advantages of the lattice Boltzmann method, which offers low-dimensional representation, and lattice gas cellular automata, which provide linear collision treatment. Building on this framework, we propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality. We validated the algorithm through comprehensive simulations of benchmark cases, including vortex-pair merging and decaying turbulence on $2048^2$ computational grid points. The results demonstrate remarkable agreement with direct numerical simulation, effectively capturing the essential nonlinear mechanisms of fluid dynamics. This work offers valuable insights into developing quantum algorithms for other nonlinear problems, and potentially advances the application of quantum computing across various transport phenomena in engineering.

Related papers

• Practical Application of the Quantum Carleman Lattice Boltzmann Method in Industrial CFD Simulations [44.99833362998488]
  This work presents a practical numerical assessment of a hybrid quantum-classical approach to CFD based on the Lattice Boltzmann Method (LBM) We evaluate this method on three benchmark cases featuring different boundary conditions, periodic, bounceback, and moving wall. Our results confirm the validity of the approach, achieving median error fidelities on the order of $10-3$ and success probabilities sufficient for practical quantum state sampling.
  arXiv  Detail & Related papers  (2025-04-17T15:41:48Z)
• Simulating Non-Markovian Dynamics in Multidimensional Electronic Spectroscopy via Quantum Algorithm [0.0]
  We present a general approach for the simulation of the optical response of multi-chromophore systems in a structured environment. A key step of the procedure is the pseudomode embedding of the system-environment problem resulting in a finite set of quantum states evolving. This formulation is then solved by a collision model integrated into a quantum algorithm designed to simulate linear and nonlinear response functions.
  arXiv  Detail & Related papers  (2024-09-09T12:13:41Z)
• Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
  This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
  arXiv  Detail & Related papers  (2024-07-04T21:11:05Z)
• Enabling Large-Scale and High-Precision Fluid Simulations on Near-Term Quantum Computers [17.27937804402152]
  Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation.
  arXiv  Detail & Related papers  (2024-06-10T07:21:23Z)
• Hybrid Stabilizer Matrix Product Operator [44.99833362998488]
  We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and Random Clifford Floquet Dynamics.
  arXiv  Detail & Related papers  (2024-05-09T18:32:10Z)
• Simulating unsteady fluid flows on a superconducting quantum processor [23.24560103938476]
  We report an experiment on the digital simulation of unsteady flows, which consists of quantum encoding, evolution, and detection of flow states. This work demonstrates the potential of quantum computing in simulating more complex flows, such as turbulence, for practical applications.
  arXiv  Detail & Related papers  (2024-04-24T13:45:43Z)
• Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes [37.69303106863453]
  We present a hybrid quantum physics-informed neural network that simulates laminar fluid flows in 3D Y-shaped mixers. Our approach combines the expressive power of a quantum model with the flexibility of a physics-informed neural network, resulting in a 21% higher accuracy compared to a purely classical neural network.
  arXiv  Detail & Related papers  (2023-04-21T20:49:29Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Potential quantum advantage for simulation of fluid dynamics [1.4046104514367475]
  We show that a potential quantum exponential speedup can be achieved to simulate the Navier-Stokes equations governing turbulence using quantum computing. This work suggests that an exponential quantum advantage may exist for simulating nonlinear multiscale transport phenomena.
  arXiv  Detail & Related papers  (2023-03-29T09:14:55Z)
• Quantum Computing for Fusion Energy Science Applications [0.0]
  We explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. We extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator and the Perron-Frobenius evolution operator. We discuss the simulation of toy models of wave-particle interactions through the simulation of quantum maps and of wave-wave interactions important in nonlinear plasma dynamics.
  arXiv  Detail & Related papers  (2022-12-09T18:56:46Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.