Characterization of photon-mediated gate errors through a perturbative approach

We develop a theoretical framework for quantifying gate fidelities in photon-mediated quantum computation architectures.

Building on and extending the Zero-Photon-Generation formalism, we derive closed-form perturbative solutions that capture both ideal (zero-order) and noisy (first-order) gate dynamics. We provide the first computationally efficient and theoretically rigorous tool for analyzing arbitrary errors in probabilistic photon-mediated gate designs. In particular, our approach unlocks the ability to incorporate coherent errors and state-dependent success probabilities in photon-mediated gates, without relying on simplifying assumptions about the noise model. We also perform numerical benchmarks showing the agreement with prior results.