Comparison of time optimal control for two level quantum systems

M. A. Jafarizadeh, Fahimeh Naghdi, M. R. Bazrafkan

Dominique Sugny

Francesca Albertini, Domenico D’Alessandro

Re-Bing Wu, Chunwen Li, Yuzhen Wang

Shuang Cong, Jie Wen, Xu‐Bo Zou

The time optimal problem for a two level quantum system is studied. We compare two different control strategies of bang-bang control and the geometric control, respectively, especially in the case of minimizing the time of steering the state from North Pole to South Pole on the Bloch sphere with bounded control. The time performances are compared for different parameters by the individual numerical simulation experiments, and the experimental results are analyzed. The results show that the geometric control spends less time than the bang-bang control does.

Francesca Albertini, Domenico D’Alessandro

We consider a two-level quantum system (quantum bit), S, which can only be controlled by modulating the difference between the two energy levels. We propose a control scheme that utilizes an additional quantum bit, A, as an auxiliary system, and obtains manipulation of S through the interaction with A. For this scheme, we derive the minimum time control for any unitary transformation on the target system S, and the form of the optimal control law. We find that the optimal time protocol involves a preliminary preparation of the state of A, the control of S using interaction with A, and no simultaneous control of S and A. The optimal time is the same as the one for a controllable two level system.