Achieving speedup in Dark Matter search experiments with a transmon-based NISQ algorithm

Coherent detection of ultralight bosonic dark matter can be achieved by monitoring slow Rabi oscillations in superconducting qubits. We introduce an ancilla-assisted, gate-based protocol that enhances sensitivity to the hidden photon kinetic mixing parameter $ε$ using a single two-qubit gate, bypassing the need to maintain long-lived multi-qubit entangled states and remaining compatible with the limitations of modern quantum hardware. We characterized the increase in sensitivity accounting for decoherence, thermal occupation, errors in readout and reset, indicating up to a ten-fold reduction in the required integration time to reach the same exclusion limit on $ε$ achievable via Rabi-sampling experiments. Under plausible hardware assumptions and three years of data taking, the projected $95\%$ C.L. exclusion limit on the hidden photon mixing parameter reaches $ε\approx 1\times 10^{-14}$ across $2.5$-$6.0$ GHz ($10$-$25$ \textmu eV).