Reliable Sample-Level Quantum Error Mitigation via Dominance-Aware Clustering
TL;DR
It is shown that nearest-center assignment, as used in clustering algorithms such as the $k$-modes algorithm, can fail to produce dominated regions even when the true centers are known, which motivates responsibility thresholding and a local dominance screen, whose combination is called dominance-aware (DA) refinement.
Abstract
Many quantum algorithms for classically difficult optimization tasks must return high-quality bitstrings from finitely many circuit executions, whereas most quantum error-mitigation methods target expectation values. We study sample-level recovery when measured probability mass is distributed around multiple latent bitstrings, called centers. Each component of the measured probability mass is called a source and we assume that each center is associated with one source. We identify dominance-at every coordinate, more than half of a retained region's probability mass comes from one source and agrees with its center-as a sufficient condition under which majority voting recovers that center with exponentially decreasing error probability. We show that nearest-center assignment, as used in clustering algorithms such as the $k$-modes algorithm, can fail to produce dominated regions even when the true centers are known. This failure motivates responsibility thresholding and a local dominance screen, whose combination we call dominance-aware (DA) refinement. Synthetic and simulated MaxCut-QAOA experiments show that DA refinement favors precision, while $k$-modes with DA refinement improves overall center recovery. All procedures are classical post-processing and require no additional quantum-circuit executions.