Learning Stabilizer-Type Constraints with Adaptive Product Measurements

Large quantum devices are most readily queried by choosing one local Pauli basis per qubit and collecting classical bitstrings. Rather than reconstructing a state or estimating preselected properties, we learn unknown stabilizer-type constraints revealed by these data and reuse them as the state of an adaptive learner. A classical compiler removes resolved directions, packs compatible unresolved directions into the next product setting, and randomly completes the remaining axes. This gives a simple exploration–exploitation loop with no graph, code, generator list, or target-family prior; before any relation is verified, it is exactly uniform Random. Across 30–64-qubit chain, graph, and code-derived targets—including independently drawn graph and CSS cohorts and a mixed state with partial constraints—the same rule completes every fixed structured run and improves on Random across all tested physically organized suites. A layered theory explains what kind of gain is possible: rare residual bottlenecks can change completion complexity; when Random is already polynomial, matching and joint capture yield repeated finite-budget gains; under an isotropic completion law, no stable directional advantage is available. Controlled interventions validate these mechanisms, and readout-noise experiments test verified feedback and targeted tail search.