Abstract
This paper studies the preparation of quantum gates that enable the realization of maximum entangled states, i.e., Bell states. A series of unitary time-evolution operators are derived to realize the Bell states through the Hadamard and CNOT gates. These operators are decomposed based on the Cartan decomposition method and steered by control laws designed based on the Lyapunov control theorem. The numerical simulations show that by adjusting proper control parameters in the designed Lyapunov-based control laws, the Hadamard and CNOT gates can be faster and better prepared through the decomposed operators, and more stable and accelerated Bell states can be achieved.
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