Decentralized Base-Graph Routing for the Quantum Internet

Abstract: Quantum repeater networks are a fundamental of any future quantum Internet and long-distance quantum communications. The entangled quantum nodes can communicate through several different levels of entanglement, leading to a heterogeneous, multi-level network structure. The level of entanglement between the quantum nodes determines the hop distance and the probability of the existence of an entangled link in the network. Here, we define a decentralized routing for entangled quantum networks. The proposed method allows an efficient routing to find the shortest paths in entangled quantum networks by using only local knowledge of the quantum nodes. We give bounds on the maximum value of the total number of entangled links of a path. The proposed scheme can be directly applied in practical quantum communications and quantum networking scenarios.

• The paper presents a novel decentralized routing approach using a base-graph structure to map entangled quantum networks.
• It leverages local node information and inverse power law distributions to efficiently determine shortest paths in multi-level networks.
• The method minimizes quantum memory usage and communication delays, enhancing long-haul quantum key distribution and experimental setups.

Decentralized Base-Graph Routing for the Quantum Internet

Introduction

The concept of a quantum Internet relies fundamentally on entangled quantum repeater networks, facilitating long-distance quantum communication through entangled links. This research introduces a decentralized routing method for entangled quantum networks, capitalizing on locally available node information to efficiently determine shortest paths within these networks. The proposed strategy focuses on managing heterogeneous, multi-level entangled networks by embedding them into a base-graph structure, optimizing pathfinding without requiring global knowledge.

Entangled Quantum Networks

Quantum nodes within this Internet model are interrelated through a spectrum of entanglement levels, forming a complex, multi-layered network architecture. The key determinant of inter-node hop distances and link probabilities is the degree of entanglement. The routing challenge is compounded by the absence of centralized knowledge, which necessitates a decentralized solution utilizing only local node interactions. The association of nodes involves quantum repeaters which act as intermediaries in this communication pathway.

Figure 1: Entangled overlay quantum network $N=\left(V,E\right)$ with heterogeneous entanglement levels.

Decentralized Routing Strategy

The novel routing approach proposed uses a base-graph $G^k$ where each node in the quantum network is mapped onto this underlying structure. This base-graph representation preserves the probabilistic nature of the entangled links and provides a scalable framework for efficient routing. The probability that specific entanglement levels exist in any edge of this graph is inversely correlated with the L1 distance of nodes, enabling decentralized decision-making for path selection.

Figure 2: $G^2$ base-graph of an overlay quantum network $N$, with entangled nodes $\phi \left(A\right)$, $\phi \left(R_i\right)$.

Quantum Base-Graph Construction

Embedding an entangled network on a base-graph involves modeling the quantum topology in a manner that reflects both node positioning and entanglement probabilities. In this framework, we deploy a probabilistic approach to infer connections between quantum nodes via an inverse power law distribution embedded in the base graph. This technique is rooted in statistical estimation methodologies, offering a practical means to achieve an optimal, network-wide mapping for efficient routing.

Implementation and Practical Benefits

The practical applicability of this approach lies in its low-complexity routing, which promises resource efficiency within quantum nodes by minimizing both quantum memory usage and auxiliary node communications. The resulting reductions in path decision-making delays render this routing scheme notable for experimental quantum networking endeavors.

Moreover, the proposed decentralized method supports long-distance quantum key distribution and facilitates advancements in experimental quantum communication frameworks by minimizing the need for complex transmission infrastructure.

Conclusion

This study contributes a feasible and efficient decentralized routing methodology for quantum Internet architecture, emphasizing the potential for practical application in long-haul quantum communication. Future quantum networks, empowered by such routing frameworks, stand to benefit from increased scalability, robustness, and reliance on resource-efficient routing strategies. This positions decentralized base-graph routing as a crucial component in the evolving landscape of quantum networking.