Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics transport phenomena within a lattice kinetic formalism. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes. The proposed simulator is amenable to realization in controlled quantum platforms, such as ion-trap quantum computers or circuit quantum electrodynamics processors.
Quantum computing shows substantial potential in accelerating simulations and alleviating memory bottlenecks in computational fluid dynamics (CFD), owing to its inherent properties of superposition and entanglement. The lattice Boltzmann method (LBM), being largely algebraic in nature, has inspired the development of various quantum LBMs. However, most existing approaches fix the relaxation time at
τ = 1, thereby confining a given mesh resolution to simulations at a single Reynolds number. Although our earlier quantum lattice kinetic scheme (LKS) lifted this restriction, it suffers from instability at high Reynolds numbers. To address this challenge, we propose a quantum fractional-step LBM (FS-LBM). In this framework, the predictor step is implemented on a quantum circuit using the standard LBM formulation, while the corrector step is performed classically. The relaxation time is retained at
τ = 1 to ensure seamless compatibility with existing quantum LBMs. Benchmark simulations of representative two- and three-dimensional incompressible isothermal and thermal flows demonstrate that the quantum FS-LBM achieves accuracy and convergence orders consistent with its classical counterpart, while significantly outperforming the quantum LKS in both precision and stability. Notably, this work presents the first quantum LBM simulation of three-dimensional incompressible thermal flows.
Abstract This work presents a fully quantum implementation of the Quantum Lattice Boltzmann Method (QLBM) for simulating one-dimensional heat conduction with internal heat generation. Building on the classical Lattice Boltzmann framework, QLBM reformulates the collision and streaming steps as unitary operations on quantum circuits, enabling site-wise parallel updates on near-term quantum hardware. In this formulation, classical distribution functions are encoded into quantum amplitudes, and the evolution of the system is performed entirely through quantum gates, including a collision operator and a streaming step realized as a qubit permutation. The model is validated by simulating a canonical diffusion problem with a localized heat source, and results are benchmarked against both classical LBM and an analytical solution obtained via ODE integration. The impact of quantum sampling noise is systematically assessed by varying the number of measurement shots, revealing that higher shot counts significantly improve fidelity to classical results. Root-mean-square error (RMSE) analyses confirm that the fully quantum model accurately captures the spatiotemporal behavior of the system, demonstrating the viability of QLBM for modeling nonunitary physics in thermally driven systems.