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High-fidelity qubit measurements play a crucial role in quantum computation,communication, and metrology. In recent experiments, it has been shown thatreadout fidelity may be improved by performing repeated quantum non-demolition(QND) readouts of a qubit's state through an ancilla. For a qubit encoded in atwo-level system, the fidelity of such schemes is limited by the fact that asingle error can destroy the information in the qubit. On the other hand, if abosonic system is used, this fundamental limit could be overcome by utilizinghigher levels such that a single error still leaves states distinguishable. Inthis work, we present a robust readout scheme, applicable to bosonic systemsdispersively coupled to an ancilla, which leverages both repeated QND readoutsand higher-level encodings to asymptotically suppress the effects ofqubit/cavity relaxation and individual measurement infidelity. We calculate themeasurement fidelity in terms of general experimental parameters, provide aninformation-theoretic description of the scheme, and describe its applicationto several encodings, including cat and binomial codes.

Robust readout of bosonic qubits in the dispersive coupling regime