Knowledge tracing framework based on the cognitive state of quantum focal element uncertainty

While quantum knowledge tracing offers significant advantages in student cognitive modeling, it remains susceptible to the quantum collapse problem, in which a quantum system's superposition states collapse into a single, deterministic state during measurement, thereby compromising the gradual nature of the learning process. To address this issue, this paper proposes QDKT, a knowledge tracing framework based on quantum focal-element uncertain cognitive states. The framework integrates quantum computing principles, Dempster-Shafer evidence theory, and deep sequential modelling techniques, constructing the QDKT-R model based on a hybrid quantum convolutional and GRU architecture and the QDKT-L model based on quantum variational circuits. The framework employs quantum focal elements as the fundamental units for cognitive state representation, utilising quantum superposition and entanglement properties to achieve a high-dimensional description of learner cognitive states, and constructs a Deng entropy-based quantum collapse detection mechanism to identify the convergence trend of quantum states toward deterministic states in long-sequence reasoning, thereby triggering corresponding state regulation strategies. Experiments on three benchmark datasets-ASSISTments2009, KDD Cup 2010, and Statics2011-demonstrate that QDKT-R achieves optimal performance with AUC scores of 0.845, 0.826, and 0.842, respectively. The experimental results indicate that the framework enhances modelling quality and provides a novel technical paradigm for the education domain.