A Comparative Analysis of Quantum Network Topologies in Context of Future Quantum Internet

Abstract

Entanglement distribution in multi node networks can become the backbone for a future quantum internet, it will become a widely accepted phenomenon as quantum repeater networks become more and more efficient. Graph theoretic approaches to make a feasible multi-node quantum network for secure communication and distributed quantum computation are of particular interest as the classical internet was built on such theories. Unlike today’s classical internet, quantum internet will most likely rely on more than one path between the source and destination. This multi-path routing paradigm allows the user-pair to establish entanglement, and send their Bell-pairs through paths other than shortest path and still get a single high fidelity Bell-pair at the end via entanglement purification. This study encompasses a quintessential comparative analysis of having more than the minimum required edges in networks to support multi-path routing with an added advantage of temporal layers from utilizing quantum memories. We provide an explanation for benefits of having redundant edges in tree networks by adding rings of edges at each level and compare the idea of cost distances with lattice networks. our analysis provides an understanding of fidelity-efficiency trade-offs in the context of user competition and path finding probabilities. We make an argument for network topologies playing an important role in serving the purpose whether it is for distributed quantum computation or for quantum key distribution. To show deployability of entanglement distribution networks with extra edges we present a wide area network for 14 selected universities in Islamabad in two different fiber-optic based network topologies. One being minimal spanning tree network that costs around $61, 370.00 and the other being completely connected network which costs about $1, 109, 670.00. Regardless of the monetary cost a clear advantage is shown in key generation rates for ideal nodes.