We have developed a quantum algorithm to solve the advection-diffusion equation (ADE) using the Lattice-Boltzmann method (LBM). This work focuses on leveraging quantum computing to improve simulations in computational fluid dynamics (CFD), starting with simpler models like the ADE, which serves as a foundation for more complex fluid dynamics problems.
Our algorithm is designed with four main steps: initialization, collision, streaming, and calculation of macroscopic properties. It is flexible enough to handle various dimensions and different velocity models. By using a special quantum data encoding method, we have made the algorithm more efficient, requiring fewer computational resources for each step. After every time step, the system is re-initialized for the next step, allowing for accurate and progressive time simulations.
We validated the algorithm by comparing its performance to classical simulations and known analytical solutions. Additionally, we demonstrated its versatility by applying it to different fluid flow scenarios, including cases with changing velocity patterns in two and three dimensions. The algorithm performed well, showing significant improvements in sampling efficiency, meaning it can achieve accurate results faster than previous methods.
This quantum algorithm is a promising step toward applying quantum computing to more complex fluid dynamics problems, setting the stage for future advancements in quantum-based simulations.
Source: https://www.sciencedirect.com/science/article/pii/S0010465524002960