Simulating fluid dynamics using hybrid quantum-classical devices

As famously stated by the Nobel laureate Richard Feynman: “…turbulence is the most important unsolved problem of classical physics….” This statement is still true today despite more than a century of research devoted to turbulence. The complicated structure of turbulent flow at small and large scales makes analysis of turbulence notoriously difficult. This proposal explores whether quantum mechanics can provide an effective framework for addressing this classical problem. The project will adapt two methods – tensor networks and analog quantum simulators - that have been used in quantum mechanics for use in computational fluid dynamics. A variety of challenging turbulent flows will be simulated, and results will be compared with those obtained using classical computational methods. The research will be integrated with education and industrial collaborations to help establish a self-sustaining ecosystem to accelerate the development of quantum technologies to solve classical problems. To leverage hybrid quantum-classical computing for addressing the complex problem of turbulence, the research will proceed along two parallel directions. First, tensor network methods will be implemented to classically simulate flows as governed by the Navier-Stokes and Fickian-Fourier reaction-convection-diffusion equations. When the classical computational complexity becomes prohibitive, the tensor networks will be uploaded to digital quantum computers, where variational quantum algorithms will be utilized. Second, an analog quantum solver based on the Koopman-von Neumann formalism will be developed to encode nonlinear partial differential equations into interacting bosonic systems. The solution of these equations will be extracted from measurements of the bosonic degrees of freedom. This approach is promising for solving the Navier-Stokes equations. Simulations of reacting flows spanning a broad range of Reynolds, Péclet, Mach, and Damköler numbers will be conducted. The extent to which the hybrid methods yield quantum advantage will be systematically assessed. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.