Abstract
The manipulation of gate operators in Non-Markovian open quantum systems are studied in this paper. A Lyapunov function based on operator distance is proposed. An additional adjustable item and the time-dependent control gain in Lyapunov control laws are used to improve control accuracy. In addition, another set of control laws is designed to maintain gate operators within given accuracy as long as possible. The proposed scheme is applied to prepare single qubit NOT gate in a two-level Non-Markovian system by the numerical simulations. The results demonstrate that the error can be limited within the level of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−4</sup> for a significant long time and the system under the proposed control law is robust against the uncertainties of system parameters.
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