Rethinking Quantum Continual Learning with Quantum Fisher Information

The paper proposes quantum elastic weight consolidation (QEWC), which uses quantum Fisher information (QFI) to estimate parameter importance from the intrinsic sensitivity of a parameterized quantum state. Simulations on variational quantum classifiers (VQCs) and sequential binary classification tasks show that unregularized sequential training causes severe forgetting, while both classical-Fisher EWC and QFI-based QEWC improve retention. The methods impose different geometries: classical Fisher information emphasizes measurement-sensitive directions, whereas QFI constrains state-geometric directions more densely. Under depolarizing noise, classical Fisher values are strongly suppressed, while QFI retains a more stable sensitivity structure.