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As quantum systems expand in size and complexity, manual qubitcharacterization and gate optimization will be a non-scalable andtime-consuming venture. Physical qubits have to be carefully calibrated becausequantum processors are very sensitive to the external environment, with controlhardware parameters slowly drifting during operation, affecting gate fidelity.Currently, existing calibration techniques require complex and lengthymeasurements to independently control the different parameters of each gate andare unscalable to large quantum systems. Therefore, fully automated protocolswith the desired functionalities are required to speed up the calibrationprocess. This paper aims to propose single-qubit calibration of superconductingqubits under continuous weak measurements from a real physical experimentalsettings point of view. We propose a real-time optimal estimator of qubitstates, which utilizes weak measurements and Bayesian optimization to find theoptimal control pulses for gate design. Our numerical results demonstrate asignificant reduction in the calibration process, obtaining a high gatefidelity. Using the proposed estimator we estimated the qubit state with andwithout measurement noise and the estimation error between the qubit state andthe estimator state is less than 0.02. With this setup, we drive anapproximated pi pulse with final fidelity of 0.9928. This shows that ourproposed strategy is robust against the presence of measurement andenvironmental noise and can also be applicable for the calibration of manyother quantum computation technologies.

Fast Quantum Calibration using Bayesian Optimization with State Parameter Estimator for Non-Markovian Environment