Connecting Dispesive Gate Sensing Experiments to Theory

Dispersive gate sensing enables fast, high-fidelity measurements of a quantum system coupled to a resonator, which can be conveniently multiplexed in the frequency domain. A quantitative comparison with the expected response from simulations can be used for aiding the interpretation and bring up of quantum devices as recently demonstrated in device designs relevant for topological qubits. To this end, it is useful to convert the change in the RF signal into a change in capacitance which is easier to access in simulations. Typically, this requires fitting a model to the RF response, but such models can be inaccurate in the presence of nearby resonances and interference processes (Fano effects) accompanied by the large magnetic fields required for topological qubits. In this work, we introduce a geometric method that leverages the symmetries inherent to dispersive readout to convert dispersive shifts into a change in capacitance with high accuracy, even in non-ideal and frequency-crowded backgrounds where resonator fitting typically breaks down.