  Several platforms are being considered as hardware for quantum technologies.
For quantum computing (QC), superconducting qubits and artificially trapped
ions are among the leading platforms, but many others also show promise, e.g.
photons, cold atoms, defect centers including Rare-Earth (RE) ions. So far,
results are limited to the regime of noisy intermediate scale qubits (NISQ),
with a small number of qubits and a limited connectivity, and it is likely that
future QC hardware will utilize several existing platforms in different ways.
Thus, it currently makes sense to invest resources broadly and explore the full
range of promising routes to quantum technology. Rare-earth ions in solids
constitute one of the most versatile platforms for future quantum technology.
One advantage is good coherence properties even when confined in strong natural
traps inside a solid-state matrix. This confinement allows very high qubit
densities and correspondingly strong ion-ion couplings. In addition, although
their fluorescence is generally weak, cavity integration can enhance the
emission greatly and enable very good connections to photonic circuits,
including at the telecom wavelengths, making them promising systems for
long-term scalability. The primary aim of this roadmap is to provide a complete
picture of what components a RE quantum computer would consist of, to describe
the details of all parts required to achieve a scalable system, and to discuss
the most promising paths to reach it. In brief, we find that clusters of 50-100
single RE ions can act as high fidelity qubits in small processors, occupying
only about (10 nm)^3. Due to the high capacity for integration of the RE
systems, they be optically read out and connected to other such clusters for
larger scalability. We make suggestions for future improvements, which could
allow the REQC platform to be a leading one.
