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Volume 5 Issue 3
May  2018

IEEE/CAA Journal of Automatica Sinica

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Nourallah Ghaeminezhad and Shuang Cong, "Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method," IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 733-740, Mar. 2018. doi: 10.1109/JAS.2018.7511084
Citation: Nourallah Ghaeminezhad and Shuang Cong, "Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method," IEEE/CAA J. Autom. Sinica, vol. 5, no. 3, pp. 733-740, Mar. 2018. doi: 10.1109/JAS.2018.7511084

Preparation of Hadamard Gate for Open Quantum Systems by the Lyapunov Control Method

doi: 10.1109/JAS.2018.7511084
Funds:

National Natural Science Foundation of China 61573330

Chinese Academy of Sciences CAS

the World Academy of Sciences TWAS

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  • In this paper, the control laws based on the Lyapunov stability theorem are designed for a two-level open quantum system to prepare the Hadamard gate, which is an important basic gate for the quantum computers. First, the density matrix interested in quantum system is transferred to vector formation. Then, in order to obtain a controller with higher accuracy and faster convergence rate, a Lyapunov function based on the matrix logarithm function is designed. After that, a procedure for the controller design is derived based on the Lyapunov stability theorem. Finally, the numerical simulation experiments for an amplitude damping Markovian open quantum system are performed to prepare the desired quantum gate. The simulation results show that the preparation of Hadamard gate based on the proposed control laws can achieve the fidelity up to 0.9985 for the different coupling strengths.

     

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