Quantum-compatible error correction using a Bayesian Dual-Gated ProbSparse transformer in discrete-variable quantum key distribution

Quantum Key Distribution (QKD) enables secure key generation with information-theoretic security guaranteed by the principles of quantum mechanics. However, achieving high reconciliation efficiency, high throughput, and low frame error rates under noisy channel conditions remains a significant challenge for practical and cost-effective Discrete-Variable Quantum Key Distribution (DV-QKD) systems. To address this issue, this research proposes a Quantum-based Bayesian Dual-Gated ProbSparse Transformer (Q-BDPT) framework for quantum-compatible error correction during the reconciliation stage of DV-QKD. Initially, a system model for DV-QKD is presented. Subsequently, an adaptive error-correction framework comprising Deep-Q-Encoder and Deep-Q-Decoder modules is developed. Unlike physical quantum error-correction codes that operate directly on qubits, the proposed framework processes measurement-derived error features, syndrome information, and channel-dependent error characteristics obtained after quantum-state transmission and measurement. The Deep-Q-Encoder and Deep-Q-Decoder are constructed using Q-BDPT with Binary Cross Entropy (BCE) loss. The proposed Q-BDPT integrates Bayesian Adversarial ProbSparse Transformer (BAPT) and Dual-Gated Spatiotemporal Attention Network (DSANet), while harmonic analysis is employed to enhance feature integration and adaptive error modelling. The framework learns probabilistic, spatial, and temporal error dependencies associated with quantum-channel behavior and generates adaptive reconciliation decisions to improve key recovery performance. Experimental results demonstrate that Q-BDPT achieves a minimum Bit Error Rate (BER) of 0.01760, a minimum Logical Error Rate (LER) of 0.00776, and a maximum Secure Key Rate (SKR) of 0.65805, thereby improving reconciliation effectiveness and secure key generation performance in DV-QKD environments.