Reconstructing quantum noise from symmetry-violating generators

By systematically introducing small symmetry-violating terms into quantum gates, we examine whether such perturbations can reproduce the tomographic noise patterns observed on actual quantum hardware. This study fits into the broader context of quantum computing and quantum information processing, where realistic noise modeling remains essential for understanding device behavior. Our analytical framework mirrors Qiskit's tomography procedures and shot model, using transparent noise control. Our results show that weak generator perturbations can reproduce average deviations in Pauli transfer matrices (PTMs) with high fidelity (given the recorded hardware noise characteristics). These findings suggest that symmetry-violating generators provide a phenomenological model for relevant classes of hardware noise. This approach offers a reproducible analytic baseline for testing noise hypotheses and calibrating simplified models against experimental data. Beyond this descriptive role, the appearance of stable symmetry-violating perturbations in the fitted models supports their use as a phenomenological description. Because the analytical framework isolates these violations at the generator level, it links native-generator perturbations to reconstructed PTM signatures. As a result, the model not only reproduces experimental process tomography data but also tests which PTM structures can be reproduced and at what perturbation magnitude, providing information for calibration, simulation, and the development of symmetry-sensitive mitigation and error-correction strategies. The present analysis is restricted to single-qubit gates.