  Photonic platforms are an excellent setting for quantum technologies because
weak photon-environment coupling ensures long coherence times. The second key
ingredient for quantum photonics is interactions between photons, which can be
provided by optical nonlinearities in the form of cross-phase-modulation (XPM).
This approach underpins many proposed applications in quantum optics and
information processing, but achieving its potential requires strong
single-photon-level nonlinear phase shifts and also scalable nonlinear
elements. In this work we show that the required nonlinearity can be provided
by exciton-polaritons in micropillars with embedded quantum wells. These
combine the strong interactions of excitons with the scalability of
micrometer-sized emitters. We observe XPM up to $3 \pm 1$ mrad per particle
using laser beams attenuated to below single photon average intensity. With our
work serving as a first stepping stone, we lay down a route for quantum
information processing in polaritonic lattices.
