Quantum reservoirs for simple fluid flows

Reservoir computing models are one way of implementing recurrent neural networks that can process sequential data. Classical reservoir computing models have been used recently with success to predict the time evolution of nonlinear dynamical systems and the low-order statistics of turbulent flows including turbulent convection flows which are driven by buoyancy forces. Here, we extend the classical model to a gate-based quantum reservoir computing model. The reservoir, which is a large sparse random network in the classical case, consists in its quantum version of a number of single-qubit random rotation gates in combination with 2-qubit entanglement gates. The performance of the model is tested for low-dimensional nonlinear Galerkin models of fluid flows, such as the Lorenz 63 model that describes two-dimensional thermal convection right above the onset of convection. The predictions, their dependence on the (hyper-)parameters of the quantum reservoir (e.g., the number of qubits), and a comparison to the classical results are presented and critically discussed.