Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including H2CS, SO3, HNCO, HFHF, N-4 and P-4. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins-N-methylacetamide-and simulate thermal relaxation and the effect of anharmonicities in H2O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH3. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.