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We apply quantum optimal control theory (QOCT) to an exactly solvablenon-Markovian open quantum bit (qubit) system to achieve state-independentquantum control and construct high-fidelity quantum gates for moderate qubitdecaying parameters. An important quantity, improvement $\mathcal{I}$, isproposed and defined to quantify the correction of gate errors due to the QOCTiteration when the environment effects are taken into account. With the help ofthe exact dynamics, we explore how the gate error is corrected in the openqubit system and determine the conditions for significant improvement. Themodel adopted in this paper can be implemented experimentally in realisticsystems such as the circuit QED system.

Optimal control of quantum gates in an exactly solvable non-Markovian open quantum bit system