In modern circuit QED architectures, superconducting transmon qubits aremeasured via the state-dependent phase and amplitude shift of a microwave fieldleaking from a coupled resonator. Determining this shift requires integratingthe field quadratures for a nonzero duration, which can permit unwantedconcurrent evolution. Here we investigate such dynamical degradation of themeasurement fidelity caused by a detuned neighboring qubit. We find that inrealistic parameter regimes, where the qubit ensemble-dephasing rate is slowerthan the qubit-qubit detuning, the joint qubit-qubit eigenstates are betterdiscriminated by measurement than the bare states. Furthermore, we show thatwhen the resonator leaks much more slowly than the qubit-qubit detuning, themeasurement tracks the joint eigenstates nearly adiabatically. However, themeasurement process also causes rare quantum jumps between the eigenstates. Therate of these jumps becomes significant if the resonator decay is comparable toor faster than the qubit-qubit detuning, thus significantly degrading themeasurement fidelity in a manner reminiscent of energy relaxation processes.
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