Tracking Dispersive Shifts Beyond the Resonance Linewidth Using Real-Time Measurement-Based Feedback

In circuit QED, dispersive readout is the established technique for measuring qubits, qudits, quantum sensors, and other quantum devices: different quantum states induce different shifts in the frequency of a coupled readout resonator. One challenge is engineering the system couplings to maximize the signal‑to‑noise ratio (SNR) of the returning microwave probe tone. Decreasing the resonator linewidth can increase SNR, but the response saturates when the dispersive shift becomes comparable to the linewidth. In a sensor, the standard technique to address this saturation is to adjust the parameters of the sensor itself--stabilizing the response--and treating the parameter adjustment as the measurement signal. However, most circuit QED resonators are designed to be fixed‑frequency and thus cannot be adjusted. Here, we address this challenge by using real-time measurement-based feedback to determine the resonance frequency and adjust our probe frequency to track the resonance. We show that this frequency-tracking can be achieved in less than one microsecond on an FPGA-based feedback system such as the Quantum Machines OPX controller. We discuss the advantages and limitations of our technique, and how it can be used for quasiparticle detection experiments and to improve qubit and qudit readout SNR.