Measurement-induced state transitions in inductively shunted transmon, part II: Theory

Dispersive measurement in superconducting qubits is performed by coupling qubits to a lossy resonator and then measuring the frequency change of that resonator by driving and occupying it with photons. The speed of readout in this scheme depends on the number of photons in the readout resonator. However, with increasing photon number qubit population can transfer to higher levels, borrowing energy from the resonator photons through resonance processes. This measurement-induced state transition (MIST) limits the speed of dispersive readout and causes qubit leakage which is detrimental to other operations and hard to reset. Here we model MIST in inductively shunted transmon (IST) qubits, and compare our results with experimental data.