Simulating fluid vortex interactions on a superconducting quantum processor

Abstract

Vortex interactions are commonly observed in atmospheric turbulence, plasma dynamics, and collective behaviors in biological systems. However, accurately simulating these complex interactions is highly challenging due to the need to capture fine-scale details over extended timescales, which places computational burdens on traditional methods. In this study, we introduce a quantum vortex method, reformulating the Navier--Stokes (NS) equations within a quantum mechanical framework to enable the simulation of multi-vortex interactions on a quantum computer. We construct the effective Hamiltonian for the vortex system and implement a spatiotemporal evolution circuit to simulate its dynamics over prolonged periods. By leveraging eight qubits on a superconducting quantum processor with gate fidelities of 99.97\% for single-qubit gates and 99.76\% for two-qubit gates, we successfully reproduce natural vortex interactions. This method bridges classical fluid dynamics and quantum computing, offering a novel computational platform for studying vortex dynamics. Our results demonstrate the potential of quantum computing to tackle longstanding challenges in fluid dynamics and broaden applications across both natural and engineering systems.