In complex online social networks, it is crucial for a service consumer to extract the trustworthiest way to a target service provider from numerous social trust paths between them. The extraction of the trustworthiest way (namely, optimal social trust path (OSTP)) with multiple end-to-end quality of trust (QoT) constraints has been proved to be NP-Complete. Heuristic algorithms with polynomial and pseudo-polynomial-time complexities are often used to deal with this challenging problem. However, existing solutions cannot guarantee the efficiency of searching, that is, they can hardly avoid obtaining partial optimal solutions during searching process. Quantum annealing uses delocalization and tunneling to avoid falling into local minima without sacrifying execution time. It has been proved to be a promising way to many optimization problems in recently published literatures. In this paper, for the first time, QA based OSTP algorithms (QA_OSTP) is applied to the extraction of the trustworthiest way. The experiment results show that QA based algorithms have better performance than its heuristic opponents.