Decay versus dephasing in Rydberg analog optimization: exchange rate, mechanism, and schedule design

Abstract

Numerical studies of noisy Rydberg-atom optimization almost universally compress decoherence into a single scalar, silently pricing spontaneous decay ($\Gamma$) and dephasing ($\gamma$) alike. We treat the two as independent axes, mapping a quantum-annealing heuristic for unit-disk maximum independent set on 20 random $N=10$ graphs across the $(\Gamma,\gamma)$ plane, with the annealing time re-optimized at every point. The mean approximation ratio does collapse onto one scalar, but onto $u=\kappa\Gamma+\gamma$ with $\kappa=8.05\pm0.5$ (stat) $\pm1.1$ (syst); the isotropic $\Gamma+\gamma$ fails by a factor of 30 in residual. First-order perturbation theory reproduces $\kappa$ from noiseless propagation alone and gives the mechanism: the objective is diagonal in the basis of the dephasing operator, so dephasing cannot change the answer once the drive is off, and a single driven atom already has $\kappa\simeq8.5$. The exchange rate is thus a property of the protocol as much as of the platform: the ramp-down fraction moves it between 2.3 and 16.3. At a fixed schedule it is stable across system sizes, interaction strengths, and estimators. Because the whole cost model is noiseless, a schedule can be tuned to a device's channel mixture without any noisy simulation: jointly tuning the drive ramp-down and the sweep's detuning ramp recovers about a third of the Markovian damage at no hardware cost, and the ramp the noise-aware objective selects is not the one noiseless optimization would choose. Per unit rate decay is eightfold the dearer channel, but the measured $T_1$ enters weighted by its branching ratio to the ground state ($b\approx0.4$ for the calibrated device), which leaves the two Lindblad channels comparably costly at a present-day operating point. One-parameter noise models remain serviceable, provided the parameter is $u$.