TrACE: Trajectory-Adaptive Error Mitigation for Variational Quantum Eigensolvers

Variational quantum eigensolvers (VQEs) use repeatedly measured energy estimates as in-loop optimization signals, making the parameter trajectory itself vulnerable to hardware noise and finite-shot fluctuations. Existing mitigation methods are limited in this regime: physics-based schemes require costly per-query executions, while offline learning-based mitigators are usually frozen pointwise predictors and can fail under the trajectory-dependent distribution shift induced by VQE. We propose **TrACE**, a trajectory-aware pretrain-and-adapt framework for in-loop VQE error mitigation. For each target Hamiltonian, TrACE pretrains a reusable mitigator within a problem-scoped ansatz pool, learning a structured mitigation prior from circuit, parameter, and noisy-measurement features. During deployment, it serves as the optimizer-facing objective and absorbs trajectory context. It is intermittently adapted without ideal-energy labels under self-supervision, updating only the fusion and output modules through repeated noisy views, trajectory stability, and weak prior anchoring. We also introduce a trajectory-level evaluation protocol that measures the quality of the parameters and convergence of VQE, rather than rewarding overly optimistic pointwise energy estimates. Across TFIM, molecular-energy, and MaxCut benchmarks, including a 100-qubit TFIM instance, TrACE improves solution quality, convergence stability, and optimization speed over representative baselines under various noise settings.