Tunable $LC$ resonator for multiplexed multi-qubit readout

This paper proposes the use of a tunable <tex>$LC$</tex> resonator to read an array of qubits in a multiplexed fashion, by making the dispersive shift of the targeted qubit dominant. Cavity and circuit electrodynamics (QED) theory is shown to support this idea. The tunable capacitor array, in parallel with a superconducting inductance, is designed to maximize the quality factor by frequency range product, <tex>$Q\cdot\Delta\omega$</tex>. This approach only requires one RF signal to measure multiple qubits, which can facilitate quantum computing scaling.