Quantum Algorithms for Fluid Simulations: Quantum Lattice-Gas Automata and Alternatives

Abstract

Quantum computing has the potential to speedup simulations exponentially. Its applicability span diverse fields such as biochemistry, cryptography and multiphysics simulations. In this work, we narrow our focus to computational fluid dynamics (CFD). We reviewed different quantum algorithms developed for fluid dynamics, discussing their advantages, disadvantages and specific characteristics. Furthermore, we have focused on the quantum lattice-gas automata (QLGA) algorithm, as it is the only model that implements nonlinear terms from Navier-Stokes equations in a natural way for a quantum computer. Positioning as the best alternative for a quantum model for CFD according to our research.

After conducting a thorough bibliographical review of various alternatives for CFD, we developed two novel quantum algorithms for fluid dynamics based on QLGA: D1Q3 (one-dimensional) and QFHP (two-dimensional). We delve into the structure, quantum circuits, and computational complexity of these algorithms. Our simulation results show the quantum noise resilience of QLGA and its capability to model Navier-Stokes equations in real use-cases such as a fluid flow between parallel plates, that we used as a benchmark. These results using QLGA are compared to the classical lattice-gas automata under different quantum noise levels and different number of measurements (shots) at the end of each time step. Given the scarcity of literature on the use lattice-gas automata (LGA) to simulate CFD problems, we also compare the accuracy of LGA with respect of the predicted results from theoretical Navier-Stokes equations. Furthermore, we also suggested two new research directions to test and develop the model, such as using a Monte-Carlo based QLGA (MCQLGA) and the first test using LGA and QLGA with an airfoil simulation. Although QLGA have problems to be solved, this work paves the way for a quantum-native algorithm for fluid dynamics capable of modelling Navier-Stokes equations at all scales with high Reynolds number with potential speedup.