Speaker
Description
The ongoing development of quantum computers may pave the way for
improvements in the state of the art of fluid and plasma simulations. While the Hamiltonian nature of quantum mechanics makes quantum computers natural tools for simulating Hamiltonian dynamics, we propose an approach to fluid dynamics that explicitly exploits the underlying Hamiltonian structure of ideal fluids.
More precisely, we consider the simulation of spectrally truncated fluid equations, such as the inviscid Burgers’ equation and the multidimensional Euler equations. We embed the nonlinear fluid dynamics into a Liouville equation defined in a configuration space, describing the linear evolution of the probability density. This linear evolution can be efficiently implemented on a digital quantum computer, as it is both linear and unitary.
The proposed quantum algorithm relies on three main steps: (i) efficient and physically motivated state preparation, (ii) Hamiltonian-based time evolution, and (iii) recovery of the original fluid variables through measurement of the averaged position of the probability density.
These results open new perspectives for encoding and simulating fluid dynamics on quantum computers, and pave the way toward the quantum simulation of ideal magnetohydrodynamics.