<p>The shortest path problem is the selection of edges for finding the optimal path between two specified nodes in a graph. There are well-known classical algorithms like Dijkstra, A*, Bellman-Ford, Floyd-Warshall, etc., although runtime grow for larger graphs. Other than the above, there are gate-based and non-gate-based quantum optimization approaches to solve in quantum computing. The problem is required to be encoded in quadratic unconstrained binary optimization and the Ising model for various quantum frameworks. In this paper to solve the shortest path problem, we have implemented models like the quantum approximate optimization algorithm known as QAOA, adiabatic quantum computing known as AQC, and quantum annealing known as QA, respectively. The models follow the unitary evolution of the Hamiltonian for the low-energy state of a solution. QAOA provides the solution by applying a sequence of quantum gates on a quantum circuit. Quantum tunneling is a basic phenomenon in both AQC and QA. The evolution cycle of the AQC and QA transforms the initial Hamiltonian to the encoded final Hamiltonian through a continuous interpolation over time. The state transformation goes through the evolution cycle for both AQC and QA. The aim of the paper demonstrates the quantum computing that can effectively encode and solve shortest path problem, with various analysis on noise effect, eigenspectra, and performance benchmark.</p>