The development of correlated quantum networks based on interconnected material nodes and quantum channels is a major challenge for the field of quantum information science, including quantum communication, computing, and metrology. Two main encodings of quantum information are generally used: a ‘discrete-variable’ encoding based for instance on single-photons and a ‘continuous-variable’ approach which relies on continuous degrees of freedom, such as the quadrature components of light modes. A mostly unexplored area is the mixing of these two approaches leading to ‘hybrid schemes’ where the advantages of both paradigms can be merged. This is the subject of the present proposal.Stated succinctly, we aim at developing the scientific and technical foundations for the realization of hybrid quantum networks with applications to the distribution and processing of quantum information. The new research activities that we propose to undertake are as follows:• The implementation of storage and subsequent rotation of a hybrid qubit• The laboratory demonstration of storage, readout and subsequent purification of continuous-variable entanglement• The experimental realization of a segment of a hybrid quantum repeaterWe will reach these objectives by developing compatible quantum light source (pulsed optical parametric oscillator) and light-matter interface (cold atoms trapped in the vicinity of elongated nanofibers) and by demonstrating novel capabilities for hybrid protocols, such as non-Gaussian state storage and quantum gates. These activities will be accompanied by a strong theoretical effort focused on the development of resource-efficient hybrid protocols for improved scaling.