# Rethinking Quantum Continual Learning with Quantum Fisher Information

arXiv: https://arxiv.org/abs/2607.16030 · HTML: https://mlsanity.com/paper/2607.16030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 17 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Continual Lifelong Learning with Neural Networks: A Review](https://mlsanity.com/paper/1802.07569/) (2018)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Measuring Catastrophic Forgetting in Neural Networks](https://mlsanity.com/paper/1708.02072/) (2017)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Validating Large-Scale Quantum Machine Learning: Efficient Simulation of Quantum Support Vector Machines Using Tensor Networks](https://mlsanity.com/paper/2405.02630/) (2024)
- [Neural-Network Heuristics for Adaptive Bayesian Quantum Estimation](https://mlsanity.com/paper/2003.02183/) (2020)
- [Quantum Continual Learning Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/2108.02786/) (2021)
- [Evaluating Continual Learning on a Home Robot](https://mlsanity.com/paper/2306.02413/) (2023)
- [Continual Learning for Autonomous Robots: A Prototype-based Approach](https://mlsanity.com/paper/2404.00418/) (2024)
- [Continual Learning Augmented Investment Decisions](https://mlsanity.com/paper/1812.02340/) (2018)
- [Quantum Pointwise Convolution: A Flexible and Scalable Approach for Neural Network Enhancement](https://mlsanity.com/paper/2412.01241/) (2024)
- [QCL-IDS: Quantum Continual Learning for Intrusion Detection with Fidelity-Anchored Stability and Generative Replay](https://mlsanity.com/paper/2601.21318/) (2026)
- [Intrinsic preservation of plasticity in continual quantum learning](https://mlsanity.com/paper/2511.17228/) (2025)

## Abstract (arXiv)

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. We propose quantum elastic weight consolidation (QEWC), a quantum Fisher information (QFI)-informed regularization method for mitigating 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 gives an information-geometric view in which 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 tasks. Simulations show that sequential training without regularization causes severe forgetting, while both CFI-based EWC and QFI-based QEWC improve retention of previous tasks. Mechanistic analyses further show 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.