Towards long-distance quantum networks with superconducting processors and optical links

We design a quantum repeater architecture, necessary for long distance quantum networks, using the recently proposed microwave cat state qubits, formed and manipulated via interaction between a superconducting nonlinear element and a microwave cavity. These qubits are especially attractive for repeaters because in addition to serving as excellent computational units with deterministic gate operations, they also have coherence times long enough to deal with the unavoidable propagation delays. Since microwave photons are too low in energy to be able to carry quantum information over long distances, as an intermediate step, we expand on a recently proposed microwave to optical transduction protocol using excited states of a rare-earth ion $mathrm{Er³⁺}$ doped crystal. To enhance the entanglement distribution rate, we propose to use spectral multiplexing by employing an array of cavities at each node. We compare our achievable rates with direct transmission and with two other promising repeater approaches, and show that ours could be higher in appropriate regimes, even in the presence of realistic imperfections and noise, while maintaining reasonably high fidelities of the final state. Thus, in the short term, our work could be directly useful for secure quantum communication, whereas in the long term, we can envision a large scale distributed quantum computing network built on our architecture.