Large-scale operations in quantum networks require efficient sorting of desired paths between nodes. In this article, we consider entanglement routing, which involves establishing an entanglement link between specific nodes in a large network of bosonic nodes. The networks are continuous-variable graph states built from finite squeezing and passive linear optics, shaped by complex network structures that mimic real-world networks. We construct a bipartite routing protocol with the specific goal of establishing a teleportation channel between two clients via passive optics operations locally operated by two different providers sharing the network. We provide criteria for extracting the aforementioned channel and, through the use of a derandomised evolutionary algorithm, extend the existing framework to study complex graph topologies.
Large-scale operations in quantum networks require efficient sorting of desired paths between nodes. In this article, we consider entanglement routing, which involves establishing an entanglement link between specific nodes in a large network of bosonic nodes. The networks are continuous-variable graph states built from finite squeezing and passive linear optics, shaped by complex network structures that mimic real-world networks. We construct a bipartite routing protocol with the specific goal of establishing a teleportation channel between two clients via passive optics operations locally operated by two different providers sharing the network. We provide criteria for extracting the aforementioned channel and, through the use of a derandomised evolutionary algorithm, extend the existing framework to study complex graph topologies.
Distributing entanglement among multiple users is a fundamental problem in quantum networks, requiring an efficient solution. In this work, a protocol is proposed for extracting maximally entangled ($|{\text{GHZ}}_{n}\ensuremath{\rangle}$) states for any number of parties in a quantum network. It is based on the graph-state formalism and requires minimal assumptions on the network state. The protocol only requires local measurements at the network nodes and just a single-qubit memory per user. Existing protocols on bipartite entanglement routing are also improved for specific nearest-neighbor network architectures. To this end, the concept of majorization is utilized to establish a hierarchy among different paths in a network based on their efficacy. This approach utilizes the symmetry of the underlying graph state to obtain better-performing algorithms.
The effective routing of entanglement over a quantum network is a fundamental problem in quantum communication. The distribution and reshaping of multipartite entanglement over a quantum network requires scalable protocols that adapt to the underlying topology. Graph states provide a convenient framework for this challenging task, as they encode global entanglement in a structured way that can be locally manipulated to produce a variety of target states, without requiring additional long-distance quantum operations. In this article, we propose graph-state-based routing protocols for sharing GHZ states, achieving larger sizes than those achieved in the existing works for given network topologies. For this improvement, we consider tree structures connecting the users participating in the final GHZ states, as opposed to the linear configurations used in the earlier works. In particular, for grid networks, we show special constructions of such trees that achieve larger GHZ states than the prior works. Moreover, if the user nodes along which the entanglement is to be routed are pre-specified, a strategy is proposed to accomplish this routing.
A quantum network promises to enable long distance quantum communication, and assemble small quantum devices into a large quantum computing cluster. Each network node can thereby be seen as a small few qubit quantum computer. Qubits can be sent over direct physical links connecting nearby quantum nodes, or by means of teleportation over pre-established entanglement amongst distant network nodes. Such pre-shared entanglement effectively forms a shortcut - a virtual quantum link - which can be used exactly once. Here, we present an abstraction of a quantum network that allows ideas from computer science to be applied to the problem of routing qubits, and manage entanglement in the network. Specifically, we consider a scenario in which each quantum network node can create EPR pairs with its immediate neighbours over a physical connection, and perform entanglement swapping operations in order to create long distance virtual quantum links. We proceed to discuss the features unique to quantum networks, which call for the development of new routing techniques. As an example, we present two simple hierarchical routing schemes for a quantum network of N nodes for a ring and sphere topology. For these topologies we present efficient routing algorithms requiring O(log N) qubits to be stored at each network node, O(polylog N) time and space to perform routing decisions, and O(log N) timesteps to replenish the virtual quantum links in a model of entanglement generation.
Complex networks structures have been extensively used for describing complex natural and technological systems, like the Internet or social networks. More recently, complex network theory has been applied to quantum systems, where complex network topologies may emerge in multiparty quantum states and quantum algorithms have been studied in complex graph structures. In this work, we study multimode Continuous Variables entangled states, named cluster states, where the entanglement structure is arranged in typical real-world complex networks shapes. Cluster states are a resource for measurement-based quantum information protocols, where the quality of a cluster is assessed in terms of the minimal amount of noise it introduces in the computation. We study optimal graph states that can be obtained with experimentally realistic quantum resources, when optimized via analytical procedure. We show that denser and regular graphs allow for better optimization. In the spirit of quantum routing, we also show the reshaping of entanglement connections in small networks via linear optics operations based on numerical optimization.
This paper proposes a novel routing protocol for distributed networks inspired by quantum entanglement. Traditional classical routing protocols suffer from inherent bottlenecks and inefficiencies, particularly as network scales increase. This work introduces an entanglement-based routing scheme that mimics the behavior of entangled particles to achieve exponentially faster and more robust routing. The core concept involves mapping network nodes to quantum states and leveraging the correlated nature of entanglement to determine optimal paths. We formulate the routing problem as a search within a complex Hilbert space, utilizing probabilistic methods to approximate the desired quantum state. The proposed protocol introduces metrics for path evaluation based on entanglement strength and distance, resulting in a dynamic routing strategy. Simulation results demonstrate the potential for significant performance improvements compared to conventional routing algorithms, offering a fundamentally new approach to network routing. Further research will focus on optimizing the algorithm for practical implementation and exploring its application in diverse network topologies.
A network of devices capable of transmitting quantum information called a quantum network has promising applications with vast benefits. One of the most near term achievable application is the quantum key distribution. It could be used for sharing a secret key between two end-users through any insecure authenticated communication channel. Other than sharing a secret key, a quantum network can be used for connecting quantum computers. Quantum computers have the potential to solve computational problems that their classical counterparts would require significantly more time to do so. By connecting such devices, distributed computation problems such as leader election or distributed consensus between nodes can be solved securely. For such applications to be put into practice on a large scale, there are open practical questions still to be answered. In a quantum network, a data qubit containing quantum information is transmitted by an operation called quantum teleportation. For it, two nodes need to share entanglement. Quantum teleportation then ensures the safe transmission of a qubit by using the shared entanglement and the exchange of two classical bits. This operation, however, consumes entanglement between the nodes, changing the network topology with each served request. In quantum networks, certain nodes share entanglement between each other. Routing in quantum networks entails determining which of these shared entanglements are used to transmit quantum information. As this proves to be a difficult task, we study quantum networks and in particular consider the problem of routing entanglement in quantum networks. The average latency for routing entanglement in a quantum network has been studied so far using a distributed routing approach. Thus, we present numerical simulation results of centralised routing for the average latency of demands in two existing entanglement generation models. In the first, shared entanglement between nodes is created on-demand. In the second, certain nodes pre-share entanglement before the demand comes. Our results show the intuition that using a centralised routing approach in the on-demand model results in drastically more average latency than in the model with pre-shared entanglement. Since some nodes might not be informed about the change in topology, we study the effect of the propagation of information about the network topology to nodes in the network. Our observations based on simulation results show that the average latency is significantly higher if the information about the topology is not propagated well in the network. As propagating information to all nodes in a network would be a significant load for the network, we consider information propagation within a radius and still observe a considerable decrease in average latency. At last, we present a technique called link prediction which can be performed by any node without the need for information propagation and still achieve a considerable decrease in average latency. It can be effectively used to predict the change of topology in a quantum network by using knowledge about the network topology for a certain future point in time and previous knowledge about the network traffic.