Quantum lattice boltzmann method advances toward practical flow simulations on non-uniform meshes

Computational fluid dynamics (CFD) is essential for aircraft design, propulsion, thermal management, and many other engineering tasks, yet high-fidelity simulations often require enormous computing resources. Quantum computing offers a potential new pathway to more efficient CFD simulations. However, efficiently mapping conventional fluid solvers onto quantum circuits remains challenging. Among current numerical approaches, the lattice Boltzmann method (LBM) is especially promising because its collision-streaming procedure has a simple algebraic form and a high degree of parallelism.

Despite this potential, most current quantum lattice Boltzmann methods face two major limitations. First, the relaxation time is commonly fixed at unity to ensure compatibility with quantum circuit operations. While this simplifies the collision process, it restricts the physical viscosity and effectively limits a given mesh resolution to a single Reynolds number. Second, the streaming step is typically realized through quantum walks, which naturally operate on uniform lattices but are difficult to extend to non-uniform meshes and curved geometries frequently encountered in practical engineering applications.

In a recent article featured in Chinese Journal of Aeronautics (https://doi.org/10.1016/j.cja.2026.104176), Prof. Liming Yang’s team from Nanjing University of Aeronautics and Astronautics proposed a quantum Taylor-series expansion and least-squares-based fractional-step lattice Boltzmann method, known as quantum TLFS-LBM. The method keeps the quantum-compatible predictor step while adding a classical diffusion-correction step to recover the target physical viscosity.

"The key idea is to preserve the components naturally compatible with quantum circuits, while introducing a fractional-step correction and a coordinate-based streaming matrix to recover the flexibility needed for practical flow simulations," the authors explained.

The team also reformulated streaming as a matrix operation on the equilibrium distribution function. Constructed using Taylor-series expansion and least-squares approximation, the streaming matrix depends only on mesh-point coordinates and can therefore be generated once for arbitrary non-uniform meshes. To enable quantum implementation, singular value decomposition is employed to decompose the resulting non-unitary matrix into a sequence of unitary operators compatible with quantum circuits. This approach enables simulations on non-uniform meshes and around curved boundaries, significantly extending the applicability of quantum LBMs.

“A single quantum circuit for the full TLFS-LBM may still demand substantial quantum resources”, the authors said. To reduce quantum-resource demands, they further introduced a multi-circuit strategy in which each circuit evolves the equilibrium distribution function along one discrete velocity direction, thereby reducing the number of qubits required for each circuit. Although the current work is validated using classical quantum simulators, reducing circuit depth and qubit count is particularly important for today’s noisy intermediate-scale quantum hardware.

The proposed method was validated using several representative two-dimensional incompressible-flow benchmark problems. Numerical results demonstrate that quantum TLFS-LBM achieves accuracy comparable to its classical counterpart while extending quantum LBMs to non-uniform meshes and complex boundaries. The mesh flexibility is especially advantageous for flows containing strong local gradients, where adaptive spatial refinement can significantly reduce unnecessary mesh points and computational cost. Meanwhile, the multi-circuit strategy further decreases the resource requirements of individual quantum circuits and improves computational efficiency.

The authors believe that this study provides a practical framework for advancing quantum LBMs toward more realistic and complex incompressible-flow simulations. However, they also candidly acknowledge that quantum TLFS-LBM is essentially a hybrid quantum-classical algorithm, involving frequent information exchange between quantum circuits and classical computation, which may affect the realization of quantum advantage. “Our team is working on developing a fully quantum implementation of TLFS-LBM,” said Prof. Liming Yang. They expect the method to provide a stronger foundation for quantum computing-enabled CFD research in the future.

Original Source

Liming Yang, Yang Xiao, Chang Shu, Yinjie Du. Quantum Taylor series expansion and least squares-based fractional-step LBM for incompressible flows on non-uniform meshes [J]. Chinese Journal of Aeronautics, 2026, 39(6):104176, https://doi.org/10.1016/j.cja.2026.104176.

About Chinese Journal of Aeronautics

Chinese Journal of Aeronautics (CJA) is an open access, peer-reviewed international journal covering all aspects of aerospace engineering, monthly published by Elsevier. The Journal reports the scientific and technological achievements and frontiers in aeronautic engineering and astronautic engineering, in both theory and practice. CJA is indexed in SCI (IF = 6.9, Q1), EI, IAA, AJ, CSA, Scopus.