KleinProbe: A Circuit-Conditioned Statistical Estimator for Effective Quantum Hardware Noise

KleinProbe defines a circuit-conditioned statistical estimator of the latent quantum hardware execution state, Θ̂(L,t), obtained from lightweight structured syndrome probes executed on the physical qubits selected by the transpiler. The estimator provides a layout-dependent characterization of the effective execution environment experienced by a specific circuit instance. The framework supports both single-layout measurements and multi-tile execution, enabling comparative observations across disjoint processor regions while maintaining a lightweight experimental footprint.