With the phenomenal explosion in online services, social networks are becoming an emerging ubiquitous platform for numerous services where service consumers require the selection of trustworthy service providers before invoking services with the help of other intermediate participants. Under this circumstance, evaluation of the trustworthiness of the service provider along the social trust paths from the service consumer to the service provider is required and to this end, selection of the optimal social trust path (OSTP) that can yield the most trustworthy evaluation result is a pre-requisite. OSTP selection with multiple quality of trust (QoT) constraints has been proven to be NP-Complete. Heuristic algorithms with polynomial and pseudo-polynomial-time complexities are often used to deal with this problem. However, existing solutions cannot guarantee the search efficiency, that is, they have difficulty in avoiding suboptimal solutions during the search process. Quantum annealing uses delocalization and tunneling to avoid local minima without sacrificing execution time. Several recent studies have proven that it is a promising way to tackle many optimization problems. In this paper, we propose a novel quantum annealing based OSTP selection algorithm (QA_OSTP) for large-scale complex social networks. Experiments show that QA_OSTP has better performance than its heuristic counterparts.