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Beyond Traditional Quantum Routing

Si-Yi Chen, Angela Sara Cacciapuoti, Marcello Caleffi

TL;DR

This work addresses the overhead and limitations of pathfinding-based quantum routing by introducing a graph-complement strategy that directly establishes end-to-end entanglement between remote nodes. It leverages multipartite graph states and graph-state operations, notably Pauli-X measurements, to transform inter-QLAN connectivity into a complement network that enables parallel servicing of multiple remote requests without centralized path discovery. The authors formalize the Inter-QLAN model, define inter-links and their complements, and present two constructive lemmas (Case I and Case II) that enable complement conversions via LOCC. Overall, the approach promises reduced delay and signaling overhead, offering a more practical route toward scalable, inter-domain quantum networks, while remaining at a preliminary stage that motivates further exploration and validation in complex topologies.

Abstract

Existing quantum routing implicitly mimics classical routing principles, with finding the ``best'' path (aka pathfinding), according to a selected routing metric, as a core mechanism for establishing end-to-end entanglement. However, optimal pathfinding is computationally intensive, particularly in complex topologies. In this paper, we propose a novel approach to quantum routing, which avoids the inherent overhead of conventional quantum pathfinding, by establishing directly entanglement between remote nodes. Our approach exploits graph complement strategies. It allows to improve the flexibility and efficiency of quantum networks, by paving the way for more practical quantum communication infrastructures.

Beyond Traditional Quantum Routing

TL;DR

This work addresses the overhead and limitations of pathfinding-based quantum routing by introducing a graph-complement strategy that directly establishes end-to-end entanglement between remote nodes. It leverages multipartite graph states and graph-state operations, notably Pauli-X measurements, to transform inter-QLAN connectivity into a complement network that enables parallel servicing of multiple remote requests without centralized path discovery. The authors formalize the Inter-QLAN model, define inter-links and their complements, and present two constructive lemmas (Case I and Case II) that enable complement conversions via LOCC. Overall, the approach promises reduced delay and signaling overhead, offering a more practical route toward scalable, inter-domain quantum networks, while remaining at a preliminary stage that motivates further exploration and validation in complex topologies.

Abstract

Existing quantum routing implicitly mimics classical routing principles, with finding the ``best'' path (aka pathfinding), according to a selected routing metric, as a core mechanism for establishing end-to-end entanglement. However, optimal pathfinding is computationally intensive, particularly in complex topologies. In this paper, we propose a novel approach to quantum routing, which avoids the inherent overhead of conventional quantum pathfinding, by establishing directly entanglement between remote nodes. Our approach exploits graph complement strategies. It allows to improve the flexibility and efficiency of quantum networks, by paving the way for more practical quantum communication infrastructures.

Paper Structure

This paper contains 11 sections, 2 theorems, 8 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Graph Complement VS Traditional Quantum Routing
  3. Traditional Quantum Routing
  4. Graph Complement Strategy
  5. Problem Statement
  6. Preliminaries
  7. Problem statement
  8. Beyond traditional quantum routing: A Graph Complement strategy
  9. Complement Inter-QLAN
  10. Conclusion
  11. Proof of Lemma \ref{['lem:x01']}

Key Result

Lemma 1

Given a bipartite graph $\ket{G_{n_1+1,n_2+1}}$ shared in an Inter-QLAN network $G_{n_1+1,n_2+1}$ such that: If the bipartite graph satisfies the above conditions, it allows to obtain a $(n_1+n_2)$-qubit bipartite graph state $\ket{\bar{G}_{n_1,n_2}}$, distributed among a complement Inter-QLAN $\bar{G}_{n_1,n_2}$, connecting each pair of complement inter-links among client-nodes. Formally: with

Figures (3)

  • Figure 1: Traditional Quantum Routing VS Graph Complement.
  • Figure 2: Pictorial illustration of research problem and main idea. Consider an Inter-QLAN network $\ket{G_{3, 4}}$ with corresponding graph $G_{3,4}=(V_1, V_2, E)$ as shown in Fig. \ref{['fig:02']}(a). Each client node $v_i \in V_1$ denote with red chip, while $v_j \in V_2$ denoted with blue chip. A set of remote interconnection requests $R$ is listed on the left Tab. III. Instead of searching for paths to satisfy each request, we transform the original Inter-QLAN network into its complement one, where all the requested node pairs in $R$ become directly connected.
  • Figure 3: Examples of Inter-QLAN and Inter-QLAN-like structures satisfying Lem.\ref{['lem:x01']} and Lem.\ref{['lem:x02']}. The Inter-QLAN $G_{4,5}$ in Fig.\ref{['fig:03.a']} and the Inter-QLAN-like structure $\tilde{G}_{4,5}$ in Fig. \ref{['fig:03.b']} are both derived from the original Inter-QLAN $G_{3,4}$ in Fig.\ref{['fig:02']}(a) by introducing two connected super-nodes, $s_1$ and $s_2$ in different QLANs. In $G_{4,5}$, the super-nodes are connected to all client nodes in the opposite QLAN, whereas in $\tilde{G}_{4,5}$, the super-nodes are connected to all client nodes in the local QLAN.

Theorems & Definitions (8)

  • Definition 1: Inter-Links
  • Definition 2: Inter-QLAN
  • Definition 3: Complement Inter-Links
  • Definition 4: Complement Inter-QLAN
  • Lemma 1
  • Lemma 2
  • Remark
  • Remark