Lyapunov-based control of a double quantum-dot qubit

The Lyapunov control theory was used in the manipulation of a single qubit in the two-level double quantum-dot (DQD) system. The proposed control process is composed of three parts: firstly a slope pulse takes the system from a positive detuning adiabatically to the anti-crossing point, which corresponds to the resonance state of the system; then a Lyapunov-based control pulse drives the charge qubit transfer non-adiabatically; finally another slope pulse takes the system away from the anti-crossing point to keep the system stable. The charge state probability P-vertical bar L > and the curve of Lyapunov-based control pulse were studied under different control parameters. Simulation results showed that: the designed Lyapunov-based control pulse has a rise time similar to 100ps, which is in the scope of the Aglient 81134A pulse generator for the implement, and it results in a significant probability 86% for transition from the initial charge state vertical bar R > to the desired target charge state vertical bar L >. Although our control scheme is designed specific for the DQD system, the technique is independent of the physical architecture and has potential for wider applications.