Time-Optimal Control of a Two Level Quantum System via Interaction With an Auxiliary System

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.