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

• URL: http://arxiv.org/abs/2608.29858v1
• Date: Sun, 30 Aug 2026 15:41:02 GMT
• Title: Decay versus dephasing in Rydberg analog optimization: exchange rate, mechanism, and schedule design
• Abstract summary: Noiseless Rydberg-atom optimization is studied in terms of decoherence and dephasing.<n>First-order perturbation theory reproduces $$ from noiseless propagation alone.<n>Because the whole cost model is noiseless, a schedule can be tuned to a device's channel mixture without any noisy simulation.
• Score: 0.05427878000393745
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Numerical studies of noisy Rydberg-atom optimization almost universally compress decoherence into a single scalar, silently pricing spontaneous decay ($Γ$) and dephasing ($γ$) 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 $(Γ,γ)$ plane, with the annealing time re-optimized at every point. The mean approximation ratio does collapse onto one scalar, but onto $u=κΓ+γ$ with $κ=8.05\pm0.5$ (stat) $\pm1.1$ (syst); the isotropic $Γ+γ$ fails by a factor of 30 in residual. First-order perturbation theory reproduces $κ$ 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 $κ\simeq8.5$. 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 $u$.

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