  We introduce an efficient scheme for the molecular dynamics of electronic systems by means of quantum Monte Carlo. The evaluation of the (Born-Oppenheimer) forces acting on the ionic positions is achieved by two main ingredients: i) the forces are computed with finite and small variance, which allows the simulation of a a large number of atoms, ii) the statistical noise corresponding to the forces is used to drive the dynamics at finite temperature by means of an appropriate friction matrix. A first application to the high-density phase of Hydrogen is given, supporting the stability of the liquid phase at = 300GP a and = 400K. 
Ab-initio molecular dynamics for high-pressure liquid Hydrogen