  We simulate the nonlinear chaotic dynamics of Lorenz-type models for a
classical two-dimensional thermal convection flow with 3 and 8 degrees of
freedom by a hybrid quantum--classical reservoir computing model. The
high-dimensional quantum reservoir dynamics are established by universal
quantum gates that rotate and entangle the individual qubits of the tensor
product quantum state. A comparison of the quantum reservoir computing model
with its classical counterpart shows that the same prediction and
reconstruction capabilities of classical reservoirs with thousands of
perceptrons can be obtained by a few strongly entangled qubits. We demonstrate
that the mean squared error between model output and ground truth in the test
phase of the quantum reservoir computing algorithm increases when the reservoir
is decomposed into separable subsets of qubits. Furthermore, the quantum
reservoir computing model is implemented on a real noisy IBM quantum computer
for up to 7 qubits. Our work thus opens the door to model the dynamics of
classical complex systems in a high-dimensional phase space effectively with an
algorithm that requires a small number of qubits.
