Maturing hybrid circuit quantum electrodynamics architectures composed of semiconductor quantum dots and on-chip microwave resonators promise an effective approach for quantum nondemolition readouts in semiconductor systems. Here, we study quantum coherence in a semiconductor charge qubit coupled with a high-impedance resonator. The qubit is controlled by a periodic pulse sequence, and a dispersive measurement is performed by measuring the time-averaged resonator response. From the Rabi oscillation and Ramsey fringe measurements, the coherence time of the charge qubit is determined as T2, Rabi ≈2.7 ns and T2, Ramsey ≈3.5 ns. Compared with the time-resolved (pulsed) measurement, this time-averaged dispersive measurement process eliminates the limitation caused by the resonator response time, enabling a high repetition rate of the pulse sequence in the experiments.
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