Efficient Quantum Network Communication using Optimized Entanglement-Swapping Trees

TL;DR

The paper addresses the challenge of long-distance quantum network communication by optimizing entanglement-swapping trees under fidelity and resource constraints, rather than relying solely on path-based routing. It introduces a formal problem framework (QNR-SP and QNR), develops a dynamic-programming approach for optimal single-tree swapping and a scalable iterative algorithm for multi-pair settings, and accompanies these with a balanced-tree heuristic and an iterative DP-based method to maintain tractable computation. Thorough NetSquid-based evaluations show order-of-magnitude improvements over prior WaitLess methods, achieving high-fidelity EPs over 500–1000 km with real-time computation readiness. Collectively, the work demonstrates that Waiting-protocol entanglement generation, when organized via optimized swapping trees, can make practical long-distance quantum networking feasible with substantial performance gains.

Abstract

Quantum network communication is challenging, as the No-cloning theorem in quantum regime makes many classical techniques inapplicable. For long-distance communication, the only viable communication approach is teleportation of quantum states, which requires a prior distribution of entangled pairs (EPs) of qubits. Establishment of EPs across remote nodes can incur significant latency due to the low probability of success of the underlying physical processes. The focus of our work is to develop efficient techniques that minimize EP generation latency. Prior works have focused on selecting entanglement paths; in contrast, we select entanglement swapping trees--a more accurate representation of the entanglement generation structure. We develop a dynamic programming algorithm to select an optimal swapping-tree for a single pair of nodes, under the given capacity and fidelity constraints. For the general setting, we develop an efficient iterative algorithm to compute a set of swapping trees. We present simulation results which show that our solutions outperform the prior approaches by an order of magnitude and are viable for long-distance entanglement generation.

Figures (14)

• Figure 1: (a) Teleportation of $|q\rangle$ from $A$ to $B$, while consuming an entangled pair $(e_1, e_2)$. (b) Entanglement swapping over the triplet of nodes $(A, B, C)$, which results in $A$'s qubit entangled with $C$'s qubit. This can be viewed as a teleportation of $e_2$ from node $B$ to $C$.
• Figure 2: A swapping tree over a path. The leaves of the tree are the path-links, which generate link-EPs continuously.
• Figure 3: Key notations used.
• Figure 4: Consider the path in (a). The imbalanced tree of (b) has a higher EP generation rate than that of the balanced tree of (c). Here, the numbers represent the EP generation rates over adjacent links or node-pairs.
• Figure 5: Qubit parameters in a swapping tree used to compute the age of a qubit $q$ at a leaf node $l(q)$. Here, $l(q)$ is the left-most leaf of the subtree $\mathcal{T}\xspace(q)$.

Theorems & Definitions (6)

• Theorem 1
• Lemma 1
• Theorem 2
• Definition 1
• Definition 2
• Definition 3