Quantum smoothed particle hydrodynamics algorithm inspired by quantum walks

Recent years have seen great progress in quantum computing, providing opportunities to overcome computational bottlenecks in many scientific applications. In particular, the intersection of computational fluid dynamics and quantum computing has become an active area of research with exponential computational speedup as an ultimate goal. In this work, we propose a quantum algorithm for the time-dependent smoothed particle hydrodynamics (SPH) method. Our algorithm uses concepts from discrete-time quantum walks to solve the one-dimensional advection partial differential equation via an SPH formalism. Hence, we construct a quantum circuit to carry out the calculations for a two-particle system over one, two, and three time steps. We compare its outputs with results from the classical SPH algorithm and show there is excellent agreement. The methodology and findings, here, are a key step toward developing a more general quantum SPH algorithm for solving practical engineering problems on gate-based quantum computers.