Optimal control of dissipative quantum systems

Dominique Sugny

Bernard Bonnard A, Dominique Sugny

Yun‐An Yan

Wei Cui

We study the optimal control problem in a non-Markovian open quantum system. The quantum system of interest is coupled to its local environment, which is dissipative in nature and tends to decay the quantum system. Based on the non-Markovian master equation, we study the non-Markovian effects on the system dynamics. The non-Markovian environment has dual effects on the quantum system: the dissipation and the backaction. The dissipation effect makes the system lose of quantum features, whereas the backaction revives it. We further design quantum control laws to control the system. The optimal control principle is studied to steer to quantum state to a target state. Finally, as an example, we used the optimal control method to control the quantum decoherence.

Zairong Xi, Wei Cui, Yu Pan

The problem of optimal control of non-Markovian open quantum system via weak measurement is presented. Based on the non-Markovian master equation, we evaluate exactly the non-Markovian effect on the dynamics of the system of interest interacting with a dissipative reservoir. We find that the non-Markovian reservoir has dual effects on the system: dissipation and backaction. The dissipation exhausts the coherence of the quantum system, whereas the backaction revives it. Moreover, we design the control Hamiltonian with the control laws attained by the stochastic optimal control and the corresponding optimal principle. At last, we considered the exact decoherence dynamics of a qubit in a dissipative reservoir composed of harmonic oscillators, and demonstrated the effectiveness of our optimal control strategy. Simulation results showed that the coherence will completely lost in the absence of control neither in non-Markovian nor Markovian system. However, the optimal feedback control steers it to a stationary stochastic process which fluctuates around the target. In this case the decoherence can be controlled effectively, which indicates that the engineered artificial reservoirs with optimal feedback control may be designed to protect the quantum coherence in quantum information and quantum computation.

Rui‐Xue Xu, YiJing Yan, Yukiyoshi Ohtsuki +2 more

An optimal control theory for open quantum systems is constructed containing non-Markovian dissipation manipulated by an external control field. The control theory is developed based on a novel quantum dissipation formulation that treats both the initial canonical ensemble and the subsequent reduced control dynamics. An associated scheme of backward propagation is presented, allowing the efficient evaluation of general optimal control problems. As an illustration, the control theory is applied to the vibration of the hydrogen fluoride molecule embedded in a non-Markovian dissipative medium. The importance of control-dissipation correlation is evident in the results.