Theoretical analysis and simulations of memory-based and all-photonic quantum repeaters and networks

Scaling quantum networks to long distances necessitates the development of advanced quantum repeater (QR) technologies. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into memory-based or all-photonic QRs; and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum networks, or a specific regime of operational parameters. This paper presents a comparative theoretical and simulation-based analysis of first-generation memory-based trapped-ion QRs and networks, and all-photonic entanglement-based QRs and networks. Our model incorporates a wide range of realistic parameters and noise sources to evaluate performance trade-offs. Major research findings of this study include: (a) the entanglement rate does not necessarily scale with the number of QRs. Although adding repeaters in a chain helps to reduce photon loss in quantum links, it also introduces overheads that can be attributed to imperfect photon collection, inefficient quantum frequency conversion, and limited detector efficiency. The entanglement rate only improves when the distance between QRs exceeds a certain threshold, specifically, when the reduction in photon loss in quantum links gained by adding QRs outweighs the inherent overheads they introduce. (b) Without quantum error correction and entanglement purification, the entanglement fidelity decreases with the number of QRs, regardless of the chain distance. Finally, the theoretical models and simulation software package developed in this study provide a versatile framework for the design and evaluation of future QR technologies, protocols, and architectures.