We propose an ab initio molecular dynamics method, capable of dramatically reducing the autocorrelation time required for the simulation of classical and quantum particles at finite temperatures. The method is based on an efficient implementation of a first order Langevin dynamics modified by means of a suitable, position dependent acceleration matrix S. Here, we apply this technique to both Lennard-Jones models, to demonstrate the accuracy and speeding-up of the sampling, and within a quantum Monte Carlo based wave function approach, for determining the phase diagram of high-pressure hydrogen with simulations much longer than the autocorrelation time. With the proposed method, we are able to equilibrate in a few hundred steps even close to the liquid-liquid phase transition (LLT). Within our approach, we find that the LLT transition is consistent with recent density functionals predicting a much larger transition pressure when the long range dispersive forces are taken into account.
