Finding an approach to actuate nonlinear optical effects at ultra-low powers and on chip-scale devices is one of the outstanding challenges in optics. The ultimate limit is the quantum regime where individual light quanta strongly interact with each other. This limit has so far been technologically impossible, but if achieved would have far-reaching consequences in information technologies. In particular, it would enable the best possible performance and wide deployment of classical nonlinear devices, and facilitate disruptive quantum information protocols that fundamentally cannot be realized on classical platforms. The primary obstacle is the weak nonlinear response of available optical materials, which necessitates high intensities and long interaction times to induce nonlinear effects.In this proposal, we will theoretically and experimentally pursue a fundamentally new paradigm – graphene-based single-photon nonlinear optics – that eliminates all of the current barriers. Our approach builds upon remarkable properties of graphene, which cause surface plasmons to be confined to scales millions of times smaller than the diffraction limit, and also induce exceptional nonlinear interaction strengths. We will show that in this unconventional nonlinear medium, even single quanta attain the requisite intensities to actuate nonlinear processes. Significantly, we aim for the first demonstration of the deterministic generation of non-classical light, which is based on "bulk" nonlinear materials rather than individual quantum emitters.The partners of GRASP are internationally recognized in the fields of graphene, nano-photonics, quantum optics, and quantum information science, and have a strong history of launching innovative multi-disciplinary research directions. This team is uniquely suited to establish graphene as the first viable route to widely deployable, chip-scale classical and quantum nonlinear optical technologies.