# Quantum Incremental Learning with Mixed State Prototypes

arXiv: https://arxiv.org/abs/2608.10464 · HTML: https://mlsanity.com/paper/2608.10464/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 27 of 27)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [Large Scale Incremental Learning](https://mlsanity.com/paper/1905.13260/) (2019)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Class-incremental learning: survey and performance evaluation on image classification](https://mlsanity.com/paper/2010.15277/) (2020)
- [Few-Shot Class-Incremental Learning](https://mlsanity.com/paper/2004.10956/) (2020)
- [Semantic Drift Compensation for Class-Incremental Learning](https://mlsanity.com/paper/2004.00440/) (2020)
- [FOSTER: Feature Boosting and Compression for Class-Incremental Learning](https://mlsanity.com/paper/2204.04662/) (2022)
- [Class-Incremental Learning: A Survey](https://mlsanity.com/paper/2302.03648/) (2023)
- [Always Be Dreaming: A New Approach for Data-Free Class-Incremental Learning](https://mlsanity.com/paper/2106.09701/) (2021)
- [FeTrIL: Feature Translation for Exemplar-Free Class-Incremental Learning](https://mlsanity.com/paper/2211.13131/) (2022)
- [Self-Sustaining Representation Expansion for Non-Exemplar Class-Incremental Learning](https://mlsanity.com/paper/2203.06359/) (2022)
- [FeCAM: Exploiting the Heterogeneity of Class Distributions in Exemplar-Free Continual Learning](https://mlsanity.com/paper/2309.14062/) (2023)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [R-DFCIL: Relation-Guided Representation Learning for Data-Free Class Incremental Learning](https://mlsanity.com/paper/2203.13104/) (2022)
- [Prototype-Sample Relation Distillation: Towards Replay-Free Continual Learning](https://mlsanity.com/paper/2303.14771/) (2023)
- [DeeSIL: Deep-Shallow Incremental Learning](https://mlsanity.com/paper/1808.06396/) (2018)
- [QSAN: A Near-term Achievable Quantum Self-Attention Network](https://mlsanity.com/paper/2207.07563/) (2022)
- [Few-shot Class-incremental Learning for Classification and Object Detection: A Survey](https://mlsanity.com/paper/2308.06764/) (2023)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [Quantum Continual Learning Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/2108.02786/) (2021)
- [Learning-based Quantum Robust Control: Algorithm, Applications and Experiments](https://mlsanity.com/paper/1702.03946/) (2017)
- [Model-free Quantum Gate Design and Calibration using Deep Reinforcement Learning](https://mlsanity.com/paper/2302.02371/) (2023)
- [Experimental measurement of Hilbert-Schmidt distance between two-qubit states as means for speeding-up machine learning](https://mlsanity.com/paper/1907.02292/) (2019)
- [Feature Entanglement-based Quantum Multimodal Fusion Neural Network](https://mlsanity.com/paper/2601.07856/) (2026)

## Abstract (arXiv)

Incremental learning models are required to learn new classes sequentially without catastrophic forgetting, while operating under parameter and memory constraints. In the Noisy Intermediate-Scale Quantum (NISQ) era, although quantum neural networks offer advantages in feature mapping, hardware limitations restrict circuit width. Furthermore, traditional quantum classifiers are constrained by the number of orthogonal basis states, limiting their capacity to accommodate a continually growing number of categories. Thus, we introduce a novel quantum incremental learning framework based on trainable mixed-state prototypes. Its original design incorporates new classes by adding class prototypes rather than increasing the circuit width of the shared quantum backbone. The use of mixed-state prototypes is another key contribution, since they have representation capabilities to represent information than a single pure-state prototype. And the decomposable mixed-state calculation provides lower production costs and a convenient Hilbert-Schmidt (HS) distance metric for classification. Simulation results show that our model achieves high-dimensional feature concentration using a minimal number of qubits, while demonstrating lower computational complexity and robust representation in incremental learning tasks compared with classical baselines.