Physics-Informed Learning of Effective Error Processes from Limited Noisy Transmon Measurements for Robust QAOA Reliability

We present a physics-informed pipeline for learning effective quantum error processes from finite-shot measurements generated by hidden transmon-like simulators. Each physical transmon is modeled as an imperfect qutrit, while the learner only receives limited tomography data rather than microscopic Hamiltonian parameters. The learned representations are compact effective models: local affine Bloch channels for each qubit and, in the three-qubit extension, pairwise residuals that capture correlated errors. The learned error models are evaluated operationally by their ability to mitigate the cost landscape of the Quantum Approximate Optimization Algorithm (QAOA) for MaxCut. A two-qubit proof of concept shows that a neural-network approach can infer a full 24-parameter effective channel from only 12 local tomography values and improve QAOA landscape reliability by about 20.4times. A scaled three-qubit study shows that local structured learning still strongly improves QAOA reliability: at K=18 local measurements, Ridge regression and the neural-network approach reduce QAOA mean absolute error from about 0.1775 to 0.0269 and 0.0306, respectively. Pair probes substantially improve correlated-error identifiability, reducing pair-residual L2 error from about 1.731 to 1.122. These results support effective error-process learning as a hardware-aware route toward more reliable variational quantum algorithms.