Effect of microwave-assisted quasiparticle tunneling on the superconducting qubit readout

Dispersive measurement of a superconducting qubit relies on the irradiation of the qubit by a microwave tone. The performance of the measurement is limited by undesired transitions between the qubit states that the tone induces. We develop a theory for a new mechanism of measurement-induced transitions, in which a readout photon and the qubit excitation are simultaneously absorbed by a Bogoliubov quasiparticle tunneling across the qubit's Josephson junction. The mechanism remains effective even in "gap engineered" qubits, whose coherence properties are otherwise insensitive to the presence of quasiparticles. We find how the probability of the quasiparticle-mediated transitions depends on the frequency of a flux-tunable transmon, as well as on the readout tone power. Our theory establishes limitations on the readout performance stemming from the presence of quasiparticles.