  Future quantum networks will enable the distribution of entanglement between
distant locations and allow applications in quantum communication, quantum
sensing and distributed quantum computation. At the core of this network lies
the ability of generating and storing entanglement at remote, interconnected
quantum nodes. While remote physical systems of various nature have been
successfully entangled, none of these realisations encompassed all of the
requirements for network operation, such as telecom-compatibility and multimode
operation. Here we report the demonstration of heralded entanglement between
two spatially separated quantum nodes, where the entanglement is stored in
multimode solid-state quantum memories. At each node a praseodymium-doped
crystal stores a photon of a correlated pair, with the second photon at
telecommunication wavelengths. Entanglement between quantum memories placed in
different labs is heralded by the detection of a telecom photon at a rate up to
1.4 kHz and is stored in the crystals for a pre-determined storage time up to
25 microseconds. We also show that the generated entanglement is robust against
loss in the heralding path, and demonstrate temporally multiplexed operation,
with 62 temporal modes. Our realisation is extendable to entanglement over
longer distances and provides a viable route towards field-deployed,
multiplexed quantum repeaters based on solid-state resources.
