Multi-shot readout error benchmark of the nitrogen-vacancy center's electronic qubit

The ground-state electronic spin of a negatively charged nitrogen-vacancy center in diamond can be used for room-temperature experiments showing coherent qubit functionality. At room temperature, photoluminescence-based qubit readout has a low single-shot fidelity; however, the populations of the qubit's two basis states can be inferred using multi-shot readout. In this work, we calculate the dependence of the error of a multi-shot inference method on various parameters of the readout process. This multi-shot readout error scales as $\Delta/\sqrt{N}$, with $N$ being the number of shots, suggesting to use the coefficient $\Delta$ as a simple multi-shot readout error benchmark. Our calculation takes into account background photons, photon loss, and initialization error. Our model enables the identification of the readout error budget, i.e., the role various imperfections play in setting the readout error. Our results enable experimentalists and engineers to focus their efforts on those hardware improvements that yield the highest performance gain for multi-shot readout.