The application of continuous quantum walks of electron on a graph composed of coupled quantum dots to molecule energy estimation is considered. The graph considered corresponds to the molecule Hamiltonian matrix. The presence of electron in each quantum dots is monitored by nearby quantum point contacts. The system is set to a state with an overlap with the ground state of the system. Then, system evolves, and finally, the ground state energy is assessed. The influence of noise produced by the point contacts on the estimation performance is also investigated.