This thesis presents a new metadynamics-based quantum Monte Carlo approach to compute the phase diagram and equilibrium properties of condensed matter systems typically quantum solids whose Hamiltonian contain important and dominant quantum effects. Two main applications are presented the classical and the quantum Ising model. Using path integral Monte Carlo we study the re-entrant phase diagram of the molecular solid hydrogen deuterium (HD) under ultra-high pressure, as the first approach for a future application of the proposed metadynamics-based MC method to calculate the free energy of this quantum system.
