Preparing entangled states by Lyapunov control

Fei Yang, Shuang Cong

James Larsen, Matthew Grace, Andrew Baczewski +1 more

Wei Yang, Jitao Sun

Zong-Xing Ding, Chang‐Sheng Hu, Li-Tuo Shen +3 more

Abstract By using the Lyapunov control approach—an optimization algorithm, we propose a dissipative scheme for efficiently preparing the three-dimensional entangled state of two Rydberg atoms, which subject to Rydberg–Rydberg interactions at the antiblockade regime. The steady target state is the unique dark state of the two-atom system, and is achieved with high fidelity under the Rydberg pumping and the atomic spontaneous emission. The time required to settle into the high-fidelity steady state is greatly accelerated by the help of Lyapunov control, which takes effects while the system is initially prepared in the states containing coherence between the dark state and decoherence-sensitive bright states. The numerical results show that a fidelity of the steady three-dimensional entangled state above 0.99 can be achieved around 2.2 ms with the current experimental conditions. We study in detail the optimal control parameters and show the robustness of the scheme against random noises. The scheme may be generalized for preparation of more complicate multi-atom entangled states.

S. Mancini, J. Wang

Cui-Yu Zhang, Mao-Fa Fang

Abstract We investigate how to prepare a Bell entangled state deterministically by using two remote superconducting qubits coupled to a coplanar waveguide resonator via Lyapunov control. The results show that when spontaneous emission of the qubits is not considered, the qubits can be completely driven to the Bell entangled state by the control fields, while the spontaneous emission of the qubits is considered, the fidelity between the prepared state and the Bell entangled state can still reach a high value even in the case with a relatively large spontaneous emission rate in qubits. We also find that stronger control fields can accelerate the evolution of the state from the initial state to the Bell entangled state. In addition, there is no doubt that the larger spontaneous emission would lead to faster decoherence, which will accelerate the system to reach the target steady state. In other words, our scheme provides an efficient way for the preparation of entangled states in superconducting systems.