Quantum continual learning aims to train quantum models on sequential tasks without losing previously learned knowledge. However, variational quantum classifiers (VQCs) are prone to catastrophic forgetting under nonstationary task distributions. To address this, we propose quantum elastic weight consolidation (QEWC), a quantum Fisher information (QFI)-informed regularization method to mitigate forgetting.
Unlike conventional elastic weight consolidation based on classical Fisher information (CFI), which measures parameter importance through measurement-dependent output statistics, QEWC uses QFI to quantify the intrinsic sensitivity of the parameterized quantum state. This provides an information-geometric perspective where important parameters are identified by the local response of the quantum state manifold.
We evaluate QEWC on VQCs trained on sequential binary classification tasks, including classical image classification and quantum phase classification. Simulations show that sequential training without regularization leads to severe forgetting, while both CFI-based EWC and QFI-based QEWC improve retention of previous tasks. Mechanistic analyses further indicate that the two methods impose different regularization geometries: CFI acts selectively on measurement-sensitive directions, whereas QFI imposes a denser state-geometric constraint over parameter space.
Under depolarizing noise, CFI values are strongly suppressed by degraded measurement statistics, while QFI preserves a more stable sensitivity structure of the noisy parameterized quantum state. These results establish QEWC as a physically motivated approach for studying and mitigating forgetting in quantum continual learning through quantum-state geometry.