Quantum Computing of Fluid Dynamics Via Hamiltonian Simulation*

It is anticipated that quantum computing will be able to tackle hard real-world problems. Fluid dynamics, a highly challenging problem in classical physics and various applications, emerges as a good candidate for showing quantum utility. We report our recent progress on quantum computing of fluid dynamics. In theory, we propose a quantum spin representation of fluid dynamics, which transforms the Navier-Stokes equation into the Schrödinger-Pauli equation through the generalized Madelung transformation. In this way, the fluid flow can be regarded as a special quantum system, which is feasible for flow simulation on a quantum computer. In terms of algorithm, we propose a quantum Hamiltonian simulation algorithm, which is able to simulate compressible or incompressible flows and scalar convection-reaction-diffusion problems with quantum acceleration. In terms of hardware implementation, we have realized the quantum simulation of two-dimensional unsteady flow on a quantum processor. These results demonstrate the potential of quantum computing to simulate complex flows, including turbulence, in future endeavors.