Benchmarking dark matter search using a parity-check protocol with machine-learning optimized pulses

We report on an improved microwave detection protocol for dark matter candidates such as the axion and the dark photon. We employ a superconducting transmon qubit dispersively coupled to a double-cavity system, enabling quantum nondemolition measurements of the photon occupation in a relatively short-lived storage cavity. To reduce the experimental cycle time and enhance sensitivity for axion and dark photon searches, we operate this detector in a regime of increased qubit--cavity coupling, resulting in Stark shifts of 4.6 MHz. In this regime, conventional control pulses suffer from strong frequency-detuning sensitivity and photon-number-dependent errors. We address this limitation by implementing frequency-detuning-robust $\ensuremath{\pi}/2$ pulses (obtained by machine-learning optimization) that preserve high-fidelity qubit control over a bandwidth of approximately 20 MHz. We experimentally validate this protocol and demonstrate single-photon detection performance comparable to prev