Quantum Incremental Learning with Mixed State Prototypes

2026-08-11

AI Summary

This work addresses the challenge of catastrophic forgetting and limited support for incremental learning in quantum neural networks during the NISQ era, primarily caused by constrained circuit width and a finite set of orthogonal basis states. To overcome these limitations, the authors propose a quantum incremental learning framework based on trainable mixed-state prototypes. By replacing pure states with mixed states, the approach enhances class representation capacity and enables the incorporation of new classes without expanding the backbone quantum circuit. A decomposable mixed-state preparation mechanism is introduced to reduce resource overhead, while classification is efficiently performed using Hilbert–Schmidt distance. Experimental results demonstrate that high-dimensional feature embeddings can be achieved with only a few qubits, yielding lower computational complexity and greater robustness compared to classical baselines.

Abstract

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.

Problem

• quantum incremental learning
• catastrophic forgetting
• mixed-state prototypes
• NISQ
• quantum classifiers

Innovation

• quantum incremental learning
• mixed-state prototypes
• NISQ
• Hilbert-Schmidt distance
• catastrophic forgetting