Influence Maximization (IM), which seeks a small set of important nodes that spread the influence widely into the network, is a fundamental problem in social networks. It finds applications in viral marketing, epidemic control, and assessing cascading failures within complex systems. Despite the huge amount of effort, finding near-optimal solutions for IM is difficult due to its NP-completeness. In this paper, we propose the first social quantum computing approaches for IM, aiming to retrieve near-optimal solutions. We propose a two-phase algorithm that 1) converts IM into a Max-Cover instance and 2) provides efficient quadratic unconstrained binary optimization formulations to solve the Max-Cover instance on quantum annealers. Our experiments on the state-of-the-art D-Wave annealer indicate better solution quality compared to classical simulated annealing, suggesting the potential of applying quantum annealing to find high-quality solutions for IM.