We present a systematic study of an ab initio simulation scheme based on damped Langevin molecular dynamics with forces statistically evaluated by means of quantum Monte Carlo. By targeting the vibrational frequencies of simple molecules, we show that all sources of systematic errors can be controlled and reliable frequencies are obtained with a reasonable computational effort. All convincing evidence fortifies our petascale simulation of liquid water. Ab initio molecular dynamics has been so far applied within the DFT framework, revealing the difficulty of current density functionals to unambiguously provide structural features, which agree with experimental observations, despite the inclusion of empirical corrections. The need for higher-level and empiricism-free reference simulations is, therefore, of great importance to provide a fully ab initio prediction of the water structure. By optimizing the code and carefully refining the calculation for the first time, an ab initi o molecular dynamics simulation of water at Variational Monte Carlo level is propagated up to sufficient time to obtain converged structural properties. We found that the calculated oxygen-oxygen and oxygen-hydrogen radial distribution functions have peak positions and shapes in fair agreements with recently reported data from neutron diffraction and X-ray scattering. Thanks to good scaling properties of QMC algorithms with the system size and fast evolving computer power, we have opened promising perspectives for future applications of our ab initio molecular dynamics.