Ensemble Fluid Simulations on Quantum Computers

We discuss the viability of ensemble simulations of fluid flows on quantum computers. The basic idea is to formulate a functional Liouville equation for the probability distribution of the flow field configuration and recognize that, due to its linearity, such an equation is in principle more amenable to quantum computing than the dynamic equations of fluid motion. After suitable marginalization and associated closure, the Liouville approach is shown to require several hundreds of logical qubits, hence calling for a major thrust in current noise correction and mitigation techniques.