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Scientific Reports

Optimal entanglement distribution within a multi-ring topology

Bogdan-Călin Ciobanu, Tudor Alexandru Calafeteanu, Alin-Bogdan Popa, Razvan Tataroiu, Pantelimon George Popescu

Published May 12, 2025• 2 citations
Publisher

Abstract

Entanglement distribution networks are essential for enabling secure, reliable, and sustained communication through the future Quantum Internet. Multi-ring network topologies offer improved scalability and redundancy, but also introduce additional routing complexity for the task of efficiently distributing entanglement. This paper solves the problem of optimal entanglement distribution in multi-ring quantum network topologies. Two separate multi-ring network configurations are analyzed, one where requests can only be routed within a single ring layer, and involves a less complex node setup, and one where requests may switch ring layers when passing through the network's nodes, at the cost of additional complexity within the nodes themselves. We propose algorithms that solve the problem of entanglement distribution in terms of optimal time needed to satisfy a set of entanglement resupply requests with given network resources, as well as the problem of optimal resources in order to satisfy a set of entanglement resupply requests within a single entanglement transmission and measurement step. We provide a comprehensive analysis of the proposed algorithms through computer simulations, which indicate that the additional complexity of a network which allows switching between ring layers brings little benefit in terms of time to serve requests, but may reduce the number of resources needed to satisfy the entanglement distribution requests in a non-blocking manner.

DOI
10.1038/s41598-025-00391-x

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Entanglement distribution networks are essential for enabling secure, reliable, and sustained communication through the future Quantum Internet. Multi-ring network topologies offer improved scalability and redundancy, but also introduce additional routing complexity for the task of efficiently distributing entanglement. This paper solves the problem of optimal entanglement distribution in multi-ring quantum network topologies. Two separate multi-ring network configurations are analyzed, one where requests can only be routed within a single ring layer, and involves a less complex node setup, and one where requests may switch ring layers when passing through the network's nodes, at the cost of additional complexity within the nodes themselves. We propose algorithms that solve the problem of entanglement distribution in terms of optimal time needed to satisfy a set of entanglement resupply requests with given network resources, as well as the problem of optimal resources in order to satisfy a set of entanglement resupply requests within a single entanglement transmission and measurement step. We provide a comprehensive analysis of the proposed algorithms through computer simulations, which indicate that the additional complexity of a network which allows switching between ring layers brings little benefit in terms of time to serve requests, but may reduce the number of resources needed to satisfy the entanglement distribution requests in a non-blocking manner.
Quantum entanglement is the most important resource in quantum networks, with no classical equivalent, and therefore, efficient entanglement distribution plays a key role in quantum communications and technologies. Optimal distribution of entanglement in a general network is a known hard problem. In this paper we analyze entanglement distribution via entanglement swapping in tree topologies showing how the problem can be reduced to chordal graph coloring. Our proposed solutions are mathematically sound for any tree network, providing polynomial-time optimal scheduling for entanglement distribution. The binary tree topology requires only one Bell State Measurement device per node, i.e. minimal hardware configuration, so, providing an optimal polynomial-time entanglement distribution algorithm for this topology establishes a fundamental building block that can be extended to more general tree topologies with diverse hardware setups. Through numerical simulation, we present a comprehensive analysis of the requests distribution per timeslot, optimal number of timeslots, variance, and running time, in terms of tree size, request distance bias, and parametrized balance in the tree topology construction. A complete optimality and complexity analysis is also provided.
Crossbar networks are a cornerstone of network architectures, capable of operating both as standalone interconnections or as integral switching components in complex, multi-stage systems. The main advantages of crossbar networks are their non-blocking operation and unparalleled minimal latency. With the advent of large scale quantum networks, crossbars might be an important asset towards the Quantum Internet. This study proposes a solution for the problem of distributing entanglement within crossbar quantum networks. Entangled particles are a consumable resource in quantum networks, and are being used by most quantum protocols. By ensuring that nodes within quantum networks are being supplied with entanglement, the reliability and efficiency of the network is maintained. By providing an efficient, scalable framework that can be used to achieve optimal entanglement distribution within crossbar quantum networks, this study offers a theoretical achievement which can be also used for enhancing quantum network performance. An algorithm for selecting an optimal entanglement distribution configuration is proposed and fully tested on realistic possible configurations.
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Quantum networks have the potential to enhance the utility of quantum protocols (for, e.g., cryptography, communication, computation, etc.) by enabling the interoperation of multiple quantum systems. In this paper, we address the distribution of entanglement to the neighbors of a central entanglement source node equipped with a number of sources of entangled photon pairs. A switching network can be an effective component connecting the central node to its neighbors, thus enabling the reconfigurable routing of generated photons. We consider optimal (in terms of insertion loss and the number of component switches) photonic switching networks designed to satisfy the particular requirements of entanglement distribution. We begin by developing a rigorous framework for the study of such entanglement-distribution switching networks. Next, we devise and apply search strategies to design optimal switching networks applicable to entanglement source nodes with 10 or fewer neighbors. Scalable switching networks are then considered for an arbitrarily large number of neighbors, resulting in asymptotically optimal switching fabrics. For all designs, we address efficient routing algorithms for determining a switching-network state that provides the entanglement distribution desired of the switching network at a given time. The combination of optimal switching-network structures and associated efficient routing algorithms addresses a key component of entanglement distribution, thus advancing the state of the art of quantum networks toward practical implementation.
Quantum networking has been attracting growing attention in both academia and industry during recent years. Although many routing protocols have been proposed to optimize the network layer of quantum networks, another key networklayer problem is under-explored: the topology design problem. Existing work is limited to using structure topologies such as a ring or grid, using randomly generated topologies, or using existing Internet backbone infrastructure. Whether these choices are desired for quantum networks is not fully explained. We propose the quantum network topology design problem, for which a set of end users are given and we need to compute a set of repeaters and their locations and connectivities while ensuring the network performance, such as throughput, is optimized under the same infrastructure cost (e.g., number of repeaters). We present the methodology of designing topologies based on the unique characteristics of entanglement distribution networks and propose an algorithm called TriPlace to compute a topology for a given set of end users in different locations of a geographic region. The simulation results show that TriPlace incurs a lower infrastructure cost than all existing solutions while achieving similar throughput performance as the best of these solutions. We believe this work will start a new research problem for quantum networks and attract more future work.
The unprecedented advancements in quantum technology have opened new prospects for the widespread adoption of quantum applications, placing new demands on the information transmission capabilities of large-scale quantum networks. Long-distance and stable entanglements are deemed as the lifeline in quantum network communication. However, some weaknesses, e.g., quantum decoherence, scarce quantum memory, and uneven-quality entanglement, of the quantum entanglement hinder the development. In this paper, we proposeSophon, an online transmission framework for quantum networks, which utilizes high-dimensional entanglements to concurrently transmit multi-qubit data to satisfy the transmission requirements of the real-time request set. We first model the quantum network with multi-qubit entanglement represented byWWWquantum state and then formulate the Entanglement Routing and Qubit Provisioning (ERQP) problem as a global-local optimization process. To solve theERQPproblem, we distributedly regard each network node as an RL agent for resource provisioning and extend the step-updating of the Markov Decision Process by introducing a centralized controller for entanglement route selection to optimize local and global objectives, respectively. Extensive simulations demonstrate, on the self-made simulation platform,Sophonachieves a21.89%−66.52%21.89\%-66.52\%21.89%−66.52%decrease in the communication cost, and is more robust on different scales of the network topology and the request set than the baselines.