Coupling Lyapunov functions approach for quantum control

Quantum control concerns driving quantum systems to the desired properties or states. This objective is hindered by the non-deterministic nature of quantum systems and the symmetric topology of the quantum state space. This paper introduces a coupling Lyapunov functions approach to counter for the stochastic nature of quantum measurements and break the symmetric topology of resulting filter state space. As an example, we then apply it to synthesize non-smooth control almost surely globally stabilizing the desired Bell state-the maximally entangled two-qubit state with various applications. It turns out that this approach enables the short time convergence of the system state, which is essential in the control of entanglement. More interestingly, its combination with the generalized concept of SWM (simultaneous weak measurement)-induced quantum state reduction allows us to deterministically generate the maximally entangled Bell state with little non-local effects. We use numerical illustration to validate the proposed scheme.