In this study, a hybrid propulsion-powered small fixed-wing unmanned aerial vehicle (UAV) was designed to enhance endurance using solar energy. The UAV, a solar-powered vertical take-off and landing (VTOL) with a 1.8 m wingspan and a take-off mass of 3.3 kg, was equipped with a propulsion system comprising solar cells, a battery, a supercapacitor and a DC/DC converter, which was modelled in MATLAB/Simulink to evaluate energy management strategies. To optimise energy utilisation, fuzzy logic (FL), equivalent consumption minimisation strategy (ECMS) and quantum particle swarm optimisation (QPSO) algorithms were implemented. Notably, the QPSO algorithm was integrated into the solar energy management system for the first time. Optimisation results indicate that the QPSO algorithm harnesses solar energy more rapidly and efficiently than other strategies, significantly improving the UAV’s endurance. The time required for the QPSO algorithm to reach maximum power is 1.7948 s and 1.5028 s, shorter than that of the FL and ECMS algorithms, respectively. This result demonstrates that the QPSO algorithm exhibits a fast dynamic response and adapts more efficiently to sudden power demands. Furthermore, considering the time required to reach the maximum power output of 77 W from the solar cell, the corresponding contributions to endurance are calculated as 1.22 h for QPSO, 0.51 h for FL and 0.06 h for ECMS.