Learning Structured Corrections through State Perturbations for Quantum Error Mitigation

Noise remains a major obstacle to the reliable execution of algorithms on quantum devices, motivating the development of quantum error mitigation (QEM) methods. Existing learning-based QEM approaches often learn a direct mapping from noisy circuit observations to mitigated measurement expected values and do not explicitly exploit the underlying structure of the mitigation problem. In this work, we introduce a different QEM framework based on pseudo perturbations of the input quantum state. By expanding the perturbation in a Pauli basis, this QEM is casted as a structured prediction problem, for which we develop a neural predictor that infers perturbation coefficients rather than directly predicting the mitigated output. To address the exponential number of Pauli basis, we derive a Pauli propagation based selection procedure. This approach identifies informative perturbation directions and constructs a reduced perturbation subspace. Experiments across diverse quantum tasks and noise settings show that our proposed framework outperform against state-of-the-art baselines.