Quantum Lattice Boltzmann Method: A Denoising Approach

  • Duong, Trong (RWTH Aachen University)
  • Möller, Matthias (Delft University of Technology)
  • Hosters, Norbert (RWTH Aachen University)

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The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While LBM is highly parallelizable on classical hardware, its translation to quantum algorithms is impeded by the collision process, which is intrinsically nonlinear and irreversible. Several existing quantum formulations implement this process requiring repeated quantum tomography and state preparation at every timestep [1,2,3], leading to significant overheads. We introduce a quantum LBM based on a denoising-type collision operator that avoids tomography-based updates. The collision dynamics are reformulated as an orthogonal projection onto the linearized manifold of equilibrium distributions around a reference state. This geometric approach filters non-equilibrium components while preserving lattice symmetries and approximating nonlinear terms needed to recover hydrodynamic behavior. A complete pipeline is presented with efficient gate-level realizations, incorporating encoding of distributions, collision, streaming, boundary conditions, and measurement of physical quantities such as hydrodynamic forces. In addition, we outline an approach for implementing projector-based operators deterministically via imaginary-time evolution [4], paving the way to fully coherent multi-timestep LBM simulations. Numerical experiments for advection–diffusion and flow problems demonstrate that the method reproduces macroscopic behaviors with high accuracy, with performance depending on the choice of reference state. REFERENCES: [1] L. Budinski, Quantum algorithm for the Navier–Stokes equations by using the streamfunctionvorticity formulation and the lattice Boltzmann method, International Journal of Quantum Information, 20(02), pp. 2150039, 2022. [2] C. Sanavio, S. Succi, Lattice Boltzmann–Carleman quantum algorithm and circuit for fluid flows at moderate Reynolds number, AVS Quantum Science, 6(2), 2024. [3] K.Y. Zeng, X.D. Niu, A. Khan, D.C. Li, H. Yamaguchi, A quantum computing-based lattice Boltzmann method with a linearized non-equilibrium collision operator and modular circuit for practical flow simulation, Physics of Fluids, 37(8), 2025. [4] Y. Suzuki, B.H. Tiang, J. Son, N.H.Y. Ng, Z. Holmes, M. Gluza, Double-bracket algorithm for quantum signal processing without post-selection, Quantum, 9, pp. 1954, 2025.