A Multi-Source Network Security Situational Awareness Approach via Fractional Calculus and Quantum State Fusion

Advanced persistent threats exploit long-range temporal dependencies and multi-source uncertainty, challenging conventional security situational awareness. This paper integrates fractional calculus, quantum state fusion, and memory-enhanced optimization to address these issues. A Caputo-derivative feature tensor captures the power-law memory decay of slow-evolving attacks. A quantum Bayesian network encodes evidence via complex probability amplitudes; a normalized interference fusion formula is rigorously derived from the density matrix, with explicit constraints that guarantee the fused probability always stays within [0,1]. A fractional-order quantum-behaved particle swarm optimization (FOQPSO) algorithm with a Mittag-Leffler memory kernel adaptively selects feature orders and fusion weights, and its convergence is formally proved using a fractional Lyapunov functional. Non-extensive Tsallis entropy (q=2) serves as a sensitive uncertainty indicator. Evaluations are conducted on KDD Cup 99 and CIC-IDS2017 using detectors whose outputs are generated according to the statistical error profiles of real-world intrusion detection systems, to eliminate evaluation circularity. A 5-fold rolling-origin × 10 random seeds protocol produces 50 independent runs. Under this protocol, the proposed FOQPSO-QBN attains a mean accuracy of 0.879 (95% CI [0.871,0.887]), a macro F1 of 0.833 (CI [0.824, 0.842]), and reduces RMSE to 0.229 (CI [0.216,0.242]). Compared with the strongest baseline, the improvement yields a large paired Cohen’s d of 1.55 and Benjamini–Hochberg adjusted p<0.001. An ARIMA-based statistical predictor is also included as a traditional time-series baseline, further confirming the superiority of the proposed memory-enhanced fusion. Ablation studies isolate the contributions of fractional features (macro F1+9.9%), quantum interference (+0.037 AUC), and the memory kernel (convergence accelerated by 35%). This framework establishes persistent memory and uncertainty reasoning for next-generation intelligent cyber defense.