Recent years have witnessed a surge of experimental and theoretical interest in controlling the properties of matter, such as its chemical reactivity, by confining it in optical cavities, where the enhancement of the light–matter coupling strength leads to the creation of hybrid light–matter states known as polaritons. However, ab initio calculations that account for the quantum nature of both the electromagnetic field and matter are challenging and have only started to be developed in recent years. We introduce a deep learning variational quantum Monte Carlo method to solve the electronic and photonic Schrödinger equations of molecules trapped in optical cavities. We extend typical electronic neural network wave function ansätze to describe joint fermionic and bosonic systems, i.e., electron–photon systems, in a quantum Monte Carlo framework. We apply our method to hydrogen molecules in a cavity, computing both ground and excited states. We assess their energy, dipole moment, charge density shift due to the cavity, the state of the photonic field, and the entanglement developed between the electrons and photons. Where possible, we compare our results with more conventional quantum chemistry methods proposed in the literature, finding good qualitative agreement, thus extending the range of scientific problems that can be tackled using machine learning techniques.
