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Intra-QLAN Connectivity: beyond the Physical Topology

Francesco Mazza, Marcello Caleffi, Angela Sara Cacciapuoti

TL;DR

This work tackles the challenge of sparse physical QLAN topologies by proposing entanglement-enabled artificial topologies that can be constructed on demand without inter-node signaling. The authors leverage graph states, notably chain and generalized tree-like graphs, distributed by an orchestrator over a star topology, and show how local Pauli measurements (e.g., $\sigma_y$, $\sigma_x$) on orchestrator qubits can realize bus and enhanced ring topologies while preserving entanglement. They introduce rigorous design constraints and provide concrete lemmas that quantify how to generate artificial links and EPR pairs, including entanglement-rolling mechanisms that swap client positions along the overlay path. The proposed framework offers robust intra-QLAN connectivity, reduces signaling delays, and provides resilience against single-point failures, contributing a novel pathway toward flexible, scalable quantum networking for the Quantum Internet.

Abstract

In the near to mid future, Quantum Local Area Networks (QLANs) -- the fundamental building block of the Quantum Internet -- will unlike exhibit physical topologies characterized by densely physical connections among the nodes. On the contrary, it is pragmatic to consider QLANs based on simpler, scarcely-connected physical topologies, such as star topologies. This constraint -- if not properly tackled -- will significantly impact the QLAN performance in terms of communication delay and/or overhead. Thankfully, it is possible to create on-demand links between QLAN nodes, without physically deploying them, by properly manipulating a shared multipartite entangled state. Thus, it is possible to build an overlay topology, referred to as artificial topology, upon the physical one. In this paper, we address the fundamental issue of engineering the artificial topology of a QLAN to bypass the limitations induced by the physical topology. The designed framework relays only on local operations, without exchanging signaling among the QLAN nodes, which, in turn, would introduce further delays in a scenario very sensitive to the decoherence. Finally, by exploiting the artificial topology, it is proved that the troubleshooting is simplified, by overcoming the single point of failure, typical of classical LAN star topologies.

Intra-QLAN Connectivity: beyond the Physical Topology

TL;DR

This work tackles the challenge of sparse physical QLAN topologies by proposing entanglement-enabled artificial topologies that can be constructed on demand without inter-node signaling. The authors leverage graph states, notably chain and generalized tree-like graphs, distributed by an orchestrator over a star topology, and show how local Pauli measurements (e.g., , ) on orchestrator qubits can realize bus and enhanced ring topologies while preserving entanglement. They introduce rigorous design constraints and provide concrete lemmas that quantify how to generate artificial links and EPR pairs, including entanglement-rolling mechanisms that swap client positions along the overlay path. The proposed framework offers robust intra-QLAN connectivity, reduces signaling delays, and provides resilience against single-point failures, contributing a novel pathway toward flexible, scalable quantum networking for the Quantum Internet.

Abstract

In the near to mid future, Quantum Local Area Networks (QLANs) -- the fundamental building block of the Quantum Internet -- will unlike exhibit physical topologies characterized by densely physical connections among the nodes. On the contrary, it is pragmatic to consider QLANs based on simpler, scarcely-connected physical topologies, such as star topologies. This constraint -- if not properly tackled -- will significantly impact the QLAN performance in terms of communication delay and/or overhead. Thankfully, it is possible to create on-demand links between QLAN nodes, without physically deploying them, by properly manipulating a shared multipartite entangled state. Thus, it is possible to build an overlay topology, referred to as artificial topology, upon the physical one. In this paper, we address the fundamental issue of engineering the artificial topology of a QLAN to bypass the limitations induced by the physical topology. The designed framework relays only on local operations, without exchanging signaling among the QLAN nodes, which, in turn, would introduce further delays in a scenario very sensitive to the decoherence. Finally, by exploiting the artificial topology, it is proved that the troubleshooting is simplified, by overcoming the single point of failure, typical of classical LAN star topologies.
Paper Structure (22 sections, 7 theorems, 67 equations, 8 figures)

This paper contains 22 sections, 7 theorems, 67 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Graph theory fundamentals
  5. Multipartite Entanglement: Graph states
  6. Model and Design Parameters
  7. System Model
  8. Graph State Type
  9. Graph State Dimensions
  10. Design Parameters
  11. From Physical to Artificial Topology
  12. Distributed State Design
  13. From Physical Star Topology to Artificial Bus Topology
  14. From Physical Star Topology to Artificial Enhanced Ring Topology
  15. Enhanced Ring: Quantifying Entanglement
  16. ...and 7 more sections

Key Result

Lemma 1

By distributing a $(2 k -1)$-qubit chain graph state through the QLAN, an artificial bus topology interconnecting $k$ clients can be obtained by performing $n_c=(k-1)$ local $\sigma_y$-Pauli measurements of the qubits retained at the orchestrator.

Figures (8)

  • Figure 1: Pictorial representation of the effects of different single-qubit Pauli-measurements on a graph state. The effects are shown by representing the graph associated with the graph state obtained after the measurements (up to local unitaries). As widely done, a graph is represented by a diagram in a plane, where vertexes are denoted by points in the plane and edges are denoted by arches between two vertices.
  • Figure 2: Pictorial representation of a QLAN. The orchestrator node (shown in red) is connected to the client nodes via a physical topology. After operations performed locally at the orchestrator, artificial topologies are built upon the physical one: artificial bus topology, in the sub-figure (b) or artificial (enhanced) ring topology, in the sub-figure (c).
  • Figure 3: Pictorial representation of chain and generalized tree-like graph states, obtained starting from a linear cluster state.
  • Figure 4: Generation of an artificial bus topology among the $k$ clients of the QLAN starting starting from a $(2k-1)$-qubit chain state. The artificial topology is obtained by (wisely) measuring each qubit retained at the orchestrator, according to Lem. \ref{['lem:01']}.
  • Figure 5: Entanglement rolling: generation of an artificial link between two clients $c_i$ and $_cj$ starting from a $(2k-1)$-qubit chain state. In the example, the clients to be interconnected within the artificial topology are $c_1$ and $c_3$,- whose proximity distant in the initially distributed chain state is $d(c_1,c_3) = 2$.
  • ...and 3 more figures

Theorems & Definitions (30)

  • Remark
  • Definition 1: Open and Closed neighborhood
  • Definition 2: Induced Subgraph
  • Definition 3: Complete graph
  • Definition 4: Star vertex
  • Definition 5: Induced star subgraph
  • Definition 6: Graph complementation
  • Definition 7: Local Complementation
  • Definition 8: Vertex deletion
  • Definition 9: Path
  • ...and 20 more