Quantum-Enhanced Deterministic Inference of $k$-Independent Set Instances on Neutral Atom Arrays

Noisy quantum annealing experiments on Rydberg atom arrays produce measurement outcomes that deviate from ideal distributions, complicating performance evaluation. To enable a data-driven benchmarking methodology for quantum devices that accounts for both solution quality and the classical computational cost of inference from noisy measurements, we introduce deterministic error mitigation (DEM), a shot-level inference procedure informed by experimentally characterized noise. We demonstrate this approach using the decision version of the $k$-independent set problem. Within a Hamming-shell framework, the DEM candidate volume is governed by the binary entropy of the bit-flip error rate, yielding an entropy-controlled classical postprocessing cost. Using experimental measurement data, DEM reduces postprocessing overhead relative to classical inference baselines. Numerical simulations and experimental results from neutral atom devices validate the predicted scaling with system size and error rate. These scalings indicate that one hour of classical computation on an Intel i9 processor corresponds to neutral atom experiments with up to $N=250-450$ atoms at effective error rates, enabling a direct, cost-based comparison between noisy quantum experiments and classical algorithms.

💡 Research Summary

The paper addresses a central challenge in near‑term quantum optimization with neutral‑atom Rydberg platforms: measurement outcomes are corrupted by readout errors, which obscure the true quality of the solutions produced by quantum annealing. To enable a fair benchmark that accounts not only for solution quality but also for the classical computational effort required to interpret noisy data, the authors introduce Deterministic Error Mitigation (DEM), a shot‑level post‑processing technique that leverages a noise model derived from experimental calibration.

The authors first observe that, on Rydberg arrays, the distribution of measured bitstrings is highly structured. Errors tend to flip individual qubits, so the Hamming distance between a measured bitstring and the ideal maximum‑independent‑set (MIS) configuration follows a binomial law. This “Hamming‑shell” picture motivates modeling the noisy output as a concentric shell around the true solution, with a probability weight that decays rapidly with increasing Hamming distance.

A minimal noise model assumes independent binary symmetric bit‑flip errors with probability (p) per site. The expected Hamming distance is (Np) and its variance (Np(1-p)). Consequently, the set of candidate configurations that need to be examined during post‑processing is essentially the Hamming ball of radius (\lceil Np\rceil). The authors derive a closed‑form estimate for the dominant search volume: \