Quantum technologies rely on materials that offer the central resource of quantum coherence, that allow one to control this resource, and that provide suitable interactions to create entanglement. Rare-earth ions (REI) doped into solids have outstanding potential in this context and could serve as a scalable, multi-functional quantum material. REI provide a unique physical system enabling a quantum register with a large number of qubits, strong dipolar interactions between the qubits allowing fast quantum gates, and coupling to optical photons – including telecom wavelengths – opening the door to connect quantum processors in a quantum network. The SQUARE project aimed at establishing individually addressable REI as a fundamental building block of a quantum computer with a photonic interface, and to overcome the basic roadblocks on the way towards scalable quantum hardware. The goal was to realize the fundamental elements of a multifunctional quantum processor node, where multiple qubits can be used for quantum storage, quantum gates, and for coherent spin-photon quantum state mapping. Within SQUARE, we worked to experimentally demonstrate key elements therefore, including efficient readout and coherent qubit control of single REI, generation of telecom single photons, and demonstrations of two-qubit gates. To guide the way towards a scalable technology, detailed simulations and refined theoretical descriptions were needed. Technology development was the second focus of SQUARE to enable scalable REI quantum computing: The proposed scheme requires highly tunable and coherent lasers to address and control multiple REI qubits, quantum-grade materials, tunable microcavities, and ultra-stable cryogenic nanopositioning systems. These elements will be directly useful for a variety of applications, ranging from other quantum technologies such as quantum communication and quantum sensing, to more general applications such as microscopy, cryogenics, and advanced spectroscopy. An overarching goal was finally to combine all the results into a roamap to guide the field. Working towards these results contributes to the development of future quantum technologies, and strengthens the European high-tech industry. At the same time, it will help to expand the leading role of European quantum research and contribute to advance quantum science.