Smart Mobility is the key component of the Smart City initiative that is being explored throughout the world. In recent years, bike-sharing systems (BSS) are being widely established in urban cities to provide a sustainable mode of transport, by fulfilling the mobility requirements of public residents. The application of BSS in highly congested urban cities reduces the effect of overcrowding, pollution, and traffic congestion problems. The crucial role behind incorporating BSS depends on the prediction and rebalancing of bike demand across all the bike stations. The bike demand prediction involves real-time analysis for identifying the discrepancy between the bike pick-up and drop-off throughout all the bike stations in a given time period. The critical part of a BSS operation is the effective management of rebalancing vehicle carrier operations that ensure bikes are restored in each station to their target value during every pick-up and drop-off operation. To enhance the prediction and rebalancing analysis of bike demand we propose quantum computing algorithms to provide computational speedup in comparison with classical algorithms. In my thesis, we focused on developing algorithms for solving prediction and combinatorial optimization problems with applications in Shared Mobility. We extensively used three methods of approach (a) Quantum Bayesian network which is quantum equivalent to classical Bayesian network for bike sharing demand prediction problems, (b) Optimization models and Quadratic unconstrained binary optimization models for solving combinatorial optimization problems such as rebalancing bike sharing systems, (c) Ensemble of prediction models with Deep learning models to measure the accuracy and computational performance of both (Quantum & Classical) computing platforms.