From classical chaotic systems to quantum qubits and qutrits

In this article, a quantum analogue of a classical chaotic system is constructed, using the Chen system and a generalized Lorenz system as an example. It is shown that if a classical system in R3 has a chaotic attractor, then a corresponding quantized system can be obtained by the density matrix theory in quantum mechanics. Furthermore, a direct transformation can be used to ensure that the basin of attraction contains the unit Bloch ball with the attractor located in its interior. As an application, a natural model for the Chen qubit is constructed and then extended to the generalized Lorenz qubit. Moreover, the Chen qutrit model is established.