Efficient and identifiable noise models for symmetry-preserving quantum circuits

Abstract Noise models support quantum-circuit simulation and need recalibration as hardware and workloads change. For circuits whose ideal outputs occupy one Hamming-weight sector, independent bit-flip (IBF) models tie leakage from the sector to the flip rate. We introduce SA-IBF, a two-parameter closed-form model whose sector-preserving weight mixes independent bit flips with flips conditioned on the sector to control this leakage separately. For nonzero weights, no mixture of product bit-flip channels reproduces its kernel. Given ideal distributions, we derive local identifiability conditions and a rank diagnostic for each fit. Across two data sets on four IBM Heron processors, SA-IBF predicts test data with lower Hellinger distance than IBF on every execution. On molecular quantum-autoencoder circuits, it matches a 21-parameter noise model fitted by Bayesian optimization to within 0.01 in Hellinger distance at three of four qubit numbers, at over 200-fold lower computational cost. This enables low-cost noise modeling of small symmetry-preserving circuits.