Fast quenches estimate partition functions because rate dials temperature: a closed-system account of anomalous accuracy on quantum annealers

A recent experiment [Le and Pelofske, arXiv:2512.19685] estimated the density of states and partition function of a 25-spin ±J Ising instance by reading raw energy histograms of D-Wave annealer samples, and highlighted a striking unexplained observation: the fastest anneals (8ns, within the coherent timescale of the device) gave the best estimates, reaching a log-relative error of 7.6 × 10−6. We show that no anomaly remains once two known ingredients are combined. First, a diabatic anneal is approximately a Boltzmann sampler whose inverse temperature βe is set by the annealing rate [Gyhm et al., arXiv:2409.18126]; we verify this in exact closed-system simulations at the experimental size n = 25, across two schedules, to sub-percent accuracy in the fast regime, and we measure the sampled ensembles to be uniform within energy shells to high precision, validating the energy-only description. Second, the raw-histogram estimator is unbiased only for a flat sampler: its bias is exactly φ(β + βe) − φ(βe) − φ(β), with φ(x) = ln⟨e−xE⟩unif, which grows linearly in βe while low-energy enrichment buys no compensating variance reduction for a Gaussian-like bulk. The fastest anneals are therefore accurate because they are nearly flat samplers sitting on the shot-noise floor; slow or strongly coupled anneals degrade exactly as observed; the interior optima in the reported cumulative sweeps are the bias–variance crossover of histogram pooling; and the headline 7.6 × 10−6 is consistent with the order statistics of a grid search over shot-noise-limited cells. The same analysis yields a free upgrade: because the schedule predicts each cell’s temperature, multi-histogram reweighting (WHAM) applies with rate-derived weights, converting the anneal-time ladder into a temperature ladder, removing the pooling bias by up to three orders of magnitude in our simulations, and extending accurate estimation toward temperatures where flat sampling fails. We state what the closed-system account does not explain as concrete, falsifiable predictions for reanalysis of the hardware data.