Parallel Segment Entanglement Swapping

TL;DR

The paper tackles the bottleneck of generating long-distance entanglement in noisy quantum networks by proposing Parallel Segment Entanglement Swapping (PSES), which segments a path and performs parallel ES between segments while executing sequential ES within composite parent nodes. It introduces a tree-like model, and two heuristic algorithms—Layer Greedy and Segment Greedy—to build the swapping structure, complemented by a central controller for time synchronization and an on-demand retransmission mechanism to handle ES failures. Quantitative definitions of node ES time cost and channel quality are provided, with formulas such as $NC = \frac{1}{(1- DPZR)\times(1- DPSR)\times CQ}$ and $CQ = 1-\frac{QLIR+\frac{QLN}{0.2}}{2}$ to capture environmental effects. Simulation results in a hierarchical quantum network show that PSES, especially Segment Greedy, achieves lower average ES time than competing strategies, and the on-demand retransmission reduces both time cost and entanglement consumption by about 80%, underscoring potential protocol-layer gains for future quantum internet architectures.

Abstract

In the noisy intermediate-scale quantum era, scientists are trying to improve the entanglement swapping success rate by researching anti-noise technology on the physical level, thereby obtaining a higher generation rate of long-distance entanglement. However, we may improve the generation rate from another perspective, which is studying an efficient entanglement swapping strategy. This paper analyzes the challenges faced by existing entanglement swapping strategies, including the node allocation principle, time synchronization, and processing of entanglement swapping failure. We present Parallel Segment Entanglement Swapping (PSES) to solve these problems. The core idea of PSES is to segment the path and perform parallel entanglement swapping between segments to improve the generation rate of long-distance entanglement. We construct a tree-like model as the carrier of PSES and propose heuristic algorithms called Layer Greedy and Segment Greedy to transform the path into a tree-like model. Moreover, we realize the time synchronization and design the on-demand retransmission mechanism to process entanglement swapping failure. The experiments show that PSES performs superiorly to other entanglement swapping strategies, and the on-demand retransmission mechanism can reduce the average entanglement swapping time by 80% and the average entanglement consumption by 80%.

Figures (8)

• Figure 1: Performing different parallel ES strategies on one path. (a) The original path consists of users (x0 and x5) and repeaters (x1, x2, x3, and x4). In the real world, the node ES time cost is mainly affected by the repeater's environmental interference (e.g., channel noise, dephasing noise, and depolarizing noise). (b) BBT transforms the path into balanced binary trees without considering node ES time cost, and the parent nodes of the same layer perform parallel ES to save time. (c) IBT transforms the path into imbalanced binary trees according to node ES time cost. (d) PSES introduces the composite parent node, consisting of several repeaters. PSES performs sequential ES inside the composite parent node and parallel ES between parent nodes of the same layer, which can fill the idle waiting time of parent nodes in the same layer for further savings.
• Figure 2: The process of time synchronization and on-demand retransmission mechanism
• Figure 3: The message flow of time synchronization and on-demand retransmission mechanism
• Figure 4: Environmental setting of experiments. The end-to-end path is extracted from the cellular topology of hierarchical architecture. A path includes the central controller, local domain controllers, classical and quantum channels, and nodes. Parallel ES strategies are deployed in the central controller to transform the path into a swapping tree.
• Figure 5: Average ES time vs. hops. The average node ES time cost is 1.4 units. The standard deviation of node ES time cost is 0.1 units.