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arXiv:2406.09963 · IEEE Transactions on Network Science and Engineering

Intra-QLAN Connectivity via Graph States: Beyond the Physical Topology

Francesco Mazza, Marcello Caleffi, Angela Sara Cacciapuoti

Published Jan 9, 2025• 14 citations
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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, namely, a graph state. Thus, it is possible to build an overlay topology, referred to asartificial topology, upon the physical one, by only performing Local Operations and Classical Communication (LOCC). 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 client nodes of the QLAN, 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.

DOI
10.1109/tnse.2024.3520856

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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, namely, a graph state. Thus, it is possible to build an overlay topology, referred to asartificial topology, upon the physical one, by only performing Local Operations and Classical Communication (LOCC). 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 client nodes of the QLAN, 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.
In Quantum Local Area Networks (QLANs) - the near-term building block of the Quantum Internet - the choice of the physical network topology is not so restrictive and binding as in classical LAN in terms of communication capabilities among the network nodes. And the rationale for this is the entanglement-enabled connectivity induced by multipartite entangled states. Indeed, it is possible to create on-demand links between the QLAN nodes by properly manipulating the shared multipartite entangled states. Thus, it is possible to build an overlay entangled network upon the physical one, characterized by a topology different from the physical one and referred to as artificial topology. In this paper we address the fundamental issue of engineering the artificial topology to bypass the limitations induced by the physical network topology. This possibility to overcome the constraints in the network design induced by the physical topology has no counterpart in classical networks. To this aim, we exploit the properties of a class of multipartite entangled states, referred to as graph states, which exhibit unique properties, making them very interesting and promising for engineering artificial topologies in QLANs.
Quantum Local Area Networks (QLANs) represent a promising building block for larger scale quantum networks with the ambitious goal -in a long time horizon- of realizing a Quantum Internet. Surprisingly, the physical topology of a QLAN can be enriched by a set of artificial links, enabled by shared multipartite entangled states among the nodes of the network. This novel concept of artificial topology revolutionizes the possibilities of connectivity within the local network, enabling an on-demand manipulation of the artificial network topology. In this paper, we discuss the implementation of the QLAN model in SeQUeNCe, a discrete-event simulator of quantum networks. Specifically, we provide an analysis of how network nodes interact, with an emphasis on the interplay between quantum operations and classical signaling within the network. Remarkably, through the modeling of a measurement protocol and a correction protocol, our QLAN model implementation enables the simulation of the manipulation process of a shared entangled quantum state, and the subsequent engineering of the entanglement-based connectivity. Our simulations demonstrate how to obtain different virtual topologies with different manipulations of the shared resources and with all the possible measurement outcomes, with an arbitrary number of nodes within the network.
The Quantum Internet is envisioned, at its final stage, to globally interconnect heterogeneous quantum networks. And this interconnection relays on entangled states shared among several quantum networks. In this paper, we take a step towards the engineering of entanglement as a inter-network resource. Specifically, we consider the interconnection of Quantum Local Area Networks (QLANs), and we show how to dynamically generate inter-QLAN artificial connectivity by means of local operations only. To this aim, we first design the multipartite entangled state to be distributed within each QLAN. Then, we show how such a state can be engineered for obtaining artificial links between different QLANs nodes. By leveraging the properties of a particular class of multipartite entangled states, namely, graph states, our results dynamically adapt the artificial connectivity to the network traffic patterns. Our proposal is preliminary towards scaling the interconnection of quantum networks.
Entanglement is unanimously recognized as the key communication resource of the Quantum Internet. Thus, the possibility of implementing unparalleled network functionalities by exploiting entanglement is gaining huge attention. However, the research efforts in this context are mainly focused onbipartite entanglement, often discarding the wide unexplored classes of entanglement shared among more than two parties, known asmultipartite entanglement. In this paper, we aim at exploiting multipartite entanglement asinter-network resource. Specifically, we consider the interconnection of different Quantum Local Area Networks (QLANs), and we show that multipartite entanglement allows to dynamically generate an inter-QLANartificialtopology, by means of local operations only, that overcomes the limitations of the physical QLAN topologies. To this aim, we first design the multipartite entangled state to be distributed within each QLAN. Then, we show how such a state can be engineered to: i) interconnect nodes belonging to different QLANs, and ii) dynamically adapt to different inter-QLAN traffic demands. Our contribution aims at providing the network engineering community with a hands-on guideline towards the concept of artificial topology and artificial neighborhood.
The Quantum Internet is commonly envisioned as a network that transports quantum states and distributes entanglement as the key resource underpinning distributed quantum applications. This view is necessary but incomplete if quantum phenomena are confined to what the network carries or manages, while network functionalities remain grounded predominantly in classical abstractions. This Perspective advances a broader thesis: quantum phenomena can also participate directly in the realization of network functionalities. We first establish the architectural baseline by introducing entanglement as a stateful network resource whose operational condition is non-locally distributed across remote nodes, evolves through manipulation or consumption, and degrades over time through decoherence. Its evolving state must therefore remain visible to the functionalities acting on it. We then move beyond resource visibility and use two mechanisms as proof points of a broader quantum-native functional design space: entanglement generation during propagation through coherent spatial-path superposition, and operational connectivity induced by shared entanglement that can depart from the physical graph. These examples show that paths, neighbors, or participating nodes may become operationally relevant in ways determined by quantum coherence and shared entanglement, rather than by physical connectivity alone. We identify Quantum Addressing as a transversal abstraction capable of representing such relations while complementing, rather than replacing, classical addressing and signaling. The resulting perspective broadens the Quantum Internet from transporting quantum information and distributing entanglement to exploiting quantum phenomena in network functioning, opening a coupled frontier spanning routing, forwarding, control, and functionality placement.
The topology of classical networks is determined by physical links between nodes, and after a network request the links are used to establish the desired connections. Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests, which can substitute links and allow one to fulfill multiple network requests with the same resource state. We utilize this to design entanglement-based quantum networks tailored to their desired functionality, independent of the underlying physical structure. The kind of entanglement to be stored is chosen to fulfill all desired network requests (i.e. parallel bipartite or multipartite communications between specific nodes chosen from some finite set), but in such a way that the storage requirement is minimized. This can be accomplished by using multipartite entangled states shared between network nodes that can be transformed by local operations to different target states. We introduce a clustering algorithm to identify connected clusters in the network for a given desired functionality, i.e. the required network topology of the entanglement-based network, and a merging algorithm that constructs multipartite entangled resource states with reduced memory requirement to fulfill all desired network requests. This leads to a significant reduction in required time and resources, and provides a powerful tool to design quantum networks that is unique to entanglement-based networks.