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

We present two protocols for constructing quantum processor nodes in randomly doped rare-earth-ion crystals and analyze their properties. By varying the doping concentration and the accessible laser tunability, the processor nodes can contain anywhere from only a few tens to almost $1000$ qubits. Furthermore, the average number of qubits each qubit can interact with, denoted by the connectivity, can be partly tailored to lie between just a few and roughly one hundred. We also study how a limited tunability of the laser affects the results, and conclude that a tuning range of $100$ GHz limits the results to roughly $100$ qubits with around $50$ connections per qubit on average. In order to construct an even larger processor, the vision is that several of these quantum processor nodes should be connected to each other in a multi-node architecture via, e.g., optical interfaces or flying qubits in the form of light. Our results are encouraging for establishing the rare-earth-ion-based systems as a quantum computing platform with strong potential and can serve to focus the efforts within the field.