Under the background of rapid development of digital economy, cross-border e-commerce has become an important engine of global trade, and the efficiency of its logistics network directly affects customer satisfaction and enterprise cost control. Aiming at the multi-objective optimization of cross-border e-commerce logistics network, this study innovatively introduces the quantum annealing algorithm, which breaks through the local optimal limitation of the traditional algorithm through the quantum tunneling effect and the superposition state characteristic, and constructs a multi-objective optimization model focusing on the logistics cost, time value and customer satisfaction. The study takes the overseas warehouse mode maritime logistics network as the object, and quantifies the multiple cost items such as storage, transportation, tax and fee through the mechanism of task decomposition and resource synergy. In the simulation example, the network robustness is verified by destruction resistance simulation. Under random attack, the network connectivity drops to 49.29% (node attack) and 56.55% (edge attack) when the node deletion ratio reaches 50%. In the deliberate attack, the improved maximum node mediator attack maintains a connectivity rate of 43.10% at a deletion ratio of 20%, which is better than the 20.79% of the traditional strategy and the 11.04% of the node-degree attack, indicating that the optimized network possesses a strong anti-interference capability. The quantum annealing algorithm has an optimal solution ratio of 79.23% in large-scale problems, which is significantly higher than the 56.19% of the genetic algorithm and the 50.18% of the heuristic algorithm, and the average number of solutions is 27.3, which is also ahead of similar algorithms. Although the CPU running time is slightly higher than that of the genetic algorithm, its global search ability and the quality of the solution have a significant advantage. This study provides support for the intelligent optimization of cross-border e-commerce logistics network and helps enterprises to reduce cost and increase efficiency and sustainable development.