AUTHOR=Liu Zhengliang , John Benzi , Emerson David R. 
  
TITLE=Quantum Lattice Boltzmann Method based on linear equilibrium distribution functions
  
JOURNAL=Frontiers in Mechanical Engineering
  
VOLUME=Volume 11 - 2025
  
YEAR=2026
  
URL=https://www.frontiersin.org/journals/mechanical-engineering/articles/10.3389/fmech.2025.1717775
  
DOI=10.3389/fmech.2025.1717775
  
ISSN=2297-3079
  
ABSTRACT=In this paper, we propose a complete formulation of the Lattice Boltzmann Method adapted for quantum computing. The classical collision, based on linear equilibrium distribution functions and streaming steps, are reformulated 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.