Speeding up dissipation-based quantum state engineering with Lyapunov control

We propose a Lyapunov control strategy to accelerate dissipative quantum state preparation by designing the control fields with respect to intermediate excited states instead of the target steady state. This approach, termed intermediate-state-based Lyapunov control (ISB-LC), allows for greater flexibility in designing control Hamiltonians and facilitates faster convergence without compromising robustness. We demonstrate the effectiveness of ISB-LC using several open quantum systems, including three-, four-, and six-level configurations, as well as entangled steady-state generation in interacting Rydberg atoms. Numerical simulations show that ISB-LC can reduce convergence times by more than an order of magnitude, offering a promising route for enhancing dissipation-based quantum control protocols.