As part of the QuantaMole consortium, we are interested in studying novel materials with extremely high nonlinearities, as well as their application as potential mediators of interactions between photons. A significant no-go result in this field is that “Single-photon Kerr nonlinearities do not help quantum computation”. We are interested in going beyond this result and study other geometries, configurations and topologies in which new materials can provide the sought-after interactions. This might include resonating geometries, utilizing χ(2) nonlinearities instead of χ(3), and new states of light in which to apply these nonlinear operations with more success.