ORIGINAL RESEARCH article
Front. Mech. Eng.
Sec. Fluid Mechanics
This article is part of the Research TopicAdvances and Applications in Lattice Boltzmann MethodView all articles
Quantum Lattice Boltzmann Method based on Linear Equilibrium Distribution Functions
Provisionally accepted
- Science and Technology Facilities Council Daresbury Laboratory, Warrington, United Kingdom
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In this paper, we propose a complete formulation of the Lattice Boltz-mann Method adapted for quantum computing. The classical collision, based on linear equilibrium distribution functions and streaming steps, are refor-mulated as linear algebraic operations. The inherently non-unitary collision operator is decomposed using Singular Value Decomposition and the Linear Combination of Unitaries technique. Bounce-back boundary conditions are incorporated directly into the collision matrix, while the streaming step is realized through conditional unitary shift operations on spatial registers, controlled by lattice velocity indices encoded in the distribution function register. This formulation ensures that the streaming step remains purely unitary. The resulting quantum circuit is implemented using Qiskit and validated against Couette flow and Poiseuille flow benchmarks. The simulation accurately reproduces the expected velocity profile, with relative errors below 10−4. This work establishes a foundational framework for quantum fluid solvers and provides a pathway toward quantum computational fluid dynamics.
Keywords: quantum computation, CFD, Lattice Boltzmann (LB) Method, Boundary condition, QISKit
Received: 02 Oct 2025; Accepted: 05 Nov 2025.
Copyright: © 2025 Liu, John and Emerson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Zhengliang Liu, liuzhengliang0219@gmail.com
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