Lyapunov Control of Quantum Systems Based on Energy-Level Connectivity Graphs

This paper proposes a new multilayer Lyapunov control scheme based on energy-level connectivity graphs of quantum systems, which enables a high-probability population transfer to any eigenstate in high-dimensional quantum systems. We provide a graph connectivity result for stability analysis and explore the selectivity characteristic of the Lyapunov control fields. A systematic layering method for the energy-level connectivity graph is presented to achieve a layer-by-layer population transfer to the target state. Several applications including a five-level quantum system, a three-qubit superconducting system, and a spin chain of five qubits are presented to demonstrate the effectiveness of the multilayer Lyapunov control method.