Nonadiabatic textit{ab initio} Quantum Dynamics without Potential Energy Surfaces

We present an efficient \textit{ab initio} algorithm for quantum dynamics simulations of interacting systems that is based on the conditional decomposition of the many-body wavefunction [Phys. Rev. Lett. 113, 083003 (2014)]. Starting with this formally exact approach, we develop a stochastic wavefunction ansatz using a set of interacting conditional wavefunctions as a basis. We show that this technique achieves quantitative accuracy for a photo-excited proton-coupled electron transfer problem and for nonequilibrium dynamics in a cavity bound electron-photon system in the ultra-strong coupling regime, using two orders of magnitude fewer trajectories than the corresponding mean field calculation. This method is highly parallelizable, and constitutes a practical and efficient alternative to available quantum-classical simulation methods for systems of interacting fermions and bosons.