Quantum Lattice Boltzmann with Denoising Collision Operators

Quantum Physics [Submitted on 11 Apr 2026] Quantum Lattice Boltzmann with Denoising Collision Operators Trong Duong, Matthias Möller, Norbert Hosters 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 translation to quantum algorithms is impeded by the collision process, which is intrinsically nonlinear and irreversible. Several existing quantum formulations implement this process through repeated quantum tomography and state preparation at every timestep, 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 without postselection, 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. Subjects: Quantum Physics (quant-ph) MSC classes: 76M28, 68Q12 Cite as: arXiv:2604.09997 [quant-ph]   (or arXiv:2604.09997v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.09997 Focus to learn more Submission history From: Trong Duong [view email] [v1] Sat, 11 Apr 2026 02:56:50 UTC (1,333 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)