A Comparison of Optimisation Algorithms for Electronic Polarisation Control in Quantum Key Distribution

Polarisation encoding is widely used in fibre-based Quantum Key Distribution (QKD), but random birefringence in optical fibres causes the transmitted states to drift, requiring active compensation at the receiver. Electronic Polarisation Controllers (EPCs) are commonly used for this purpose, yet the relationship between their control voltages and the resulting polarisation transformation is highly nonlinear and difficult to model. While optimisation algorithms are frequently employed to align and stabilise polarisation states, their comparative performance has not been systematically studied in realistic QKD settings. In this work, we benchmark four optimisation algorithms for electronic polarisation control, using both a numerical model and a 50 km fibre-based experimental setup. We evaluate each algorithm in terms of convergence time, failure rate, and stability, under both initial alignment and continuous drift compensation scenarios. Coordinate Descent achieved the fastest average alignment time (2.1 ms in simulation; 34.6 s experimentally), while Simulated Annealing delivered perfect reliability. We further propose a hybrid control strategy that combines fast initial alignment with high-reliability realignment. This approach was validated over a continuous 2 h QKD simulation with real fibre drift, demonstrating robust polarisation control without manual intervention. Our results provide guidance for algorithm selection in practical QKD deployments and suggest a pathway to resilient, autonomous polarisation tracking in long-distance quantum networks.