Benchmarking the readout of a superconducting qubit for repeated measurements

Readout of superconducting qubits faces a trade-off between measurement speed and unwanted back-action on the qubit caused by the readout drive, such as T₁ degradation and leakage out of the computational subspace. The readout is typically benchmarked by integrating the readout signal and choosing a binary threshold to extract the "readout fidelity". We show that such a characterization may significantly overlook readout-induced leakage errors. We introduce a method to quantitatively assess this error by repeatedly executing a composite operation -- a readout preceded by a randomized qubit-flip. We apply this technique to characterize the dispersive readout of an intrinsically Purcell-protected qubit. We report a binary readout fidelity of $99.63%$ and quantum non-demolition (QND) fidelity exceeding $99.00%$ which takes into account a leakage error rate of 0.12±0.03%, under a repetition rate of (380 ns)⁻¹ for the composite operation.