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We present two protocols for constructing quantum processor nodes in randomlydoped rare-earth-ion crystals and analyze their properties. By varying thedoping concentration and the accessible laser tunability, the processor nodescan contain anywhere from only a few tens to almost $1000$ qubits. Furthermore,the average number of qubits each qubit can interact with, denoted by theconnectivity, can be partly tailored to lie between just a few and roughly onehundred. We also study how a limited tunability of the laser affects theresults, and conclude that a tuning range of $100$ GHz limits the results toroughly $100$ qubits with around $50$ connections per qubit on average. Inorder to construct an even larger processor, the vision is that several ofthese quantum processor nodes should be connected to each other in a multi-nodearchitecture via, e.g., optical interfaces or flying qubits in the form oflight. Our results are encouraging for establishing the rare-earth-ion-basedsystems as a quantum computing platform with strong potential and can serve tofocus the efforts within the field.

High connectivity quantum processor nodes using single-ion-qubits in rare-earth-ion-doped crystals