Quantum Incremental Learning Uses Mixed States for New Classes

This research addresses the challenges of incremental learning in the Noisy Intermediate-Scale Quantum (NISQ) era, where quantum neural networks face hardware limitations in circuit width and traditional quantum classifiers are constrained by the number of orthogonal basis states. The paper proposes a novel quantum incremental learning framework that enables models to learn new classes sequentially without experiencing catastrophic forgetting, all while operating under strict parameter and memory constraints. The core innovation lies in the use of trainable mixed-state prototypes. Unlike previous approaches that might require expanding the quantum circuit for each new class, this framework incorporates new classes by simply adding class prototypes. Mixed-state prototypes are a key contribution, offering superior representation capabilities compared to single pure-state prototypes. Furthermore, the decomposable calculation of mixed states provides lower production costs and a convenient Hilbert-Schmidt (HS) distance metric for classification. Simulation results indicate that this model can achieve high-dimensional feature concentration using a minimal number of qubits, demonstrating robust representation and lower computational complexity in incremental learning tasks when compared to classical baselines.