Robust readout of bosonic qubits in the dispersive coupling regime

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