Asynchronous Entanglement Routing for the Quantum Internet

TL;DR

The paper tackles quantum-native routing for the Quantum Internet by replacing synchronized, phase-based path discovery with asynchronous routing that maintains a distributed instant topology (via DODAG or spanning-tree structures). It formalizes the routing problem under local knowledge and probabilistic entanglement generation/swapping, and derives rate expressions showing asynchronous schemes can outperform synchronous ones, with gains that grow with coherence time $T_{co}$. The authors develop two distributed schemes (DODAG and distributed GHS-based spanning tree), analyze their time complexities, and validate them through large-grid simulations, showing higher entanglement rates and robustness to decoherence. They also provide geometric insights (via triangle analysis) that explain when asynchronous routing yields advantages, and discuss practical implications for designing scalable quantum networks and networks of networks. The work suggests prioritizing DODAG-based asynchronous routing for near-term quantum networks and outlines future directions such as hierarchical DODAGs, multi-root architectures, and non-grid topologies.

Abstract

With the emergence of the Quantum Internet, the need for advanced quantum networking techniques has significantly risen. Various models of quantum repeaters have been presented, each delineating a unique strategy to ensure quantum communication over long distances. We focus on repeaters that employ entanglement generation and swapping. This revolves around establishing remote end-to-end entanglement through repeaters, a concept we denote as the "quantum-native" repeaters (also called "first-generation" repeaters in some literature). The challenges in routing with quantum-native repeaters arise from probabilistic entanglement generation and restricted coherence time. Current approaches use synchronized time slots to search for entanglement-swapping paths, resulting in inefficiencies. Here, we propose a new set of asynchronous routing protocols for quantum networks by incorporating the idea of maintaining a dynamic topology in a distributed manner, which has been extensively studied in classical routing for lossy networks, such as using a destination-oriented directed acyclic graph (DODAG) or a spanning tree. The protocols update the entanglement-link topology asynchronously, identify optimal entanglement-swapping paths, and preserve unused direct-link entanglements. Our results indicate that asynchronous protocols achieve a larger upper bound with an appropriate setting and significantly higher entanglement rate than existing synchronous approaches, and the rate increases with coherence time, suggesting that it will have a much more profound impact on quantum networks as technology advances.

Figures (17)

• Figure 1: Single-hop entanglement generation via entanglement swapping. Alice and Bob intend to establish an end-to-end entanglement through a repeater positioned in between. The process involves two steps: (1) both parties create an entangled state with the repeater, resulting in two pairs of entangled qubits: Alice's $\ket{q_1}$ paired with the repeater's $\ket{r_1}$ and Bob's $\ket{q_2}$ paired with the repeater's $\ket{r_2}$. (2) the repeater conducts entanglement swapping, which essentially performs the Bell state measurement on $\ket{r_1}$ and $\ket{r_2}$ (see Subsection \ref{['subsection:swapping']}) assisted by classical communication, producing an end-to-end entanglement between Alice's $\ket{q_1}$ and Bob's $\ket{q_2}$.
• Figure 2: End-to-end entanglement generation. Nodes A and C in the network intend to establish an end-to-end entanglement. (a) The network consists of nodes connected by optical communication links, forming the physical topology. (b) In the external phase, nodes connected by the same optical link attempt to generate direct-link entanglement, resulting in an instant topology of entanglement links (the orange helical links). For example, Nodes A and D are connected by the entanglement link $E_{AD}$. (c) In the internal phase, all repeaters involved in two pairs of entanglements perform entanglement swapping on the qubits closer to the source or destination. Node E, for instance, has four qubits, with each qubit entangled with one of its four neighboring nodes ($E_{DE}$, $E_{HE}$, $E_{EF}$, and $E_{EC}$). It performs swapping on $\ket{q_1}$ and $\ket{q_2}$ since they are connected to the nodes closer to A and C, respectively. (d) By consuming all entanglements in the instant topology, A and C successfully obtain an end-to-end entanglement. Since each node is only aware of itself and its neighbor's entanglement-link statuses, Node E does not know if the path A-D-E-C would succeed. It also performs swapping on $\ket{q_3}$ and $\ket{q_4}$ to increase the success rate of achieving an end-to-end entanglement.
• Figure 3: The circuit of entanglement swapping.
• Figure 4: An example purification circuit with link capacity two.
• Figure 5: A link between Alice and Bob with capacity two.