QuSSET: Shot Set Encoder for Quantum Property Estimation of Variable-Length States

Estimating many observables from a small measurement record is difficult when each new quantum state can be sampled only a few times. We ask whether measurements from one variational-circuit family can support property estimation across both observables and system lengths. is a noncausal, variable-length shot-set encoder that preserves spatial order within each shot while aggregating repeated shots as an exchangeable set. Masked-outcome pretraining learns an ansatz-specific prior from unlabeled random-Pauli records without property labels or circuit parameters. Separate supervised heads then map the same property-agnostic records to either a symmetric isotropic spin-correlation matrix or an antisymmetric Dzyaloshinskii–Moriya (DM) correlation matrix. Pretraining and supervision use only lengths $L\le 16$; the resulting estimators are evaluated without further adaptation on new states at $L=18,20$, using 64 shots per state. On a depth-4 long-range circuit family, QuSSET outperforms learned and calibrated statistical estimators using the same records, as well as deterministic estimators granted separately acquired, target-specific measurements, across both observables. Crucially, this advantage persists at the unseen lengths \(L=18,20\): without length-specific adaptation, each estimator processes longer shot records and predicts correlation matrices larger than any encountered during training. Matched controls show that masked pretraining provides its largest benefit with few labels and a persistent gain for long-range correlations. Together, these results show that one ansatz-level measurement corpus and pretrained initialization can support distinct property estimators and extrapolate to chain lengths absent from training.