Fig. 1: Schematic of three-level ensemble descriptions for lattice gas.
From: Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics
a Velocity-level ensemble, corresponding classical LBM; b node-level ensemble, corresponding to our QLBM; c lattice-level ensemble, corresponding to LGCA. The lattice \({\mathcal{L}}\) comprises N discrete nodes (black dots). Each node represents a local flow state, and it consists of q = 4 cells (red circles) for the D2Q4 model. Each card (containing nodes) represents a realization. The probability of each realization is depicted by the saturation level of circles in (a) and the saturation level of cards in (b, c). Our QLBM is featured by the medium dimensionality (computational cost) and linear collision treatment (quantum compatibility), suitable for an efficient quantum algorithm. The particle collision in LBM in (a) involves nonlinear calculations with probability values for different cells, whereas the collision in our QLBM in (b) or LGCA in (c) is characterized by a linear combination of different realizations.
