Dispersive readout of multi-level quantum circuits.
The readout of superconducting quantum circuit is often performed using a dispersive measurement scheme. In such scheme, a quantum superconducting circuit is connected to an LC-oscillator, so that the resonance frequency of the latter acquires a small dispersive shift, whose magnitude depends on the quantum state of the former. Unfortunately, in the case of a two-level quantum circuit, the measurement fidelity of a dispersive scheme suffers from the poor compromise between the magnitude of the dispersive shift and the rate of spontaneous emission of the qubit circuit into the LC-circuit. This is because both quantities grow simultaneously as the qubit-oscillator system approaches the vacuum Rabi resonance (when the qubit frequency matches the LC-frequency). However, the frustrating link between the rate of spontaneous emission and the magnitude of the dispersive shift can be easily broken with a multi-level quantum circuit. There, the dispersive shift of the qubit transition may originate from the vacuum Rabi resonances involving transitions other than the qubit one, while the spontaneous emission depends only on the proximity to the vacuum Rabi resonance involving the qubit transition. We illustrate this idea using an example of the fluxonium artificial atom.