Efficient routing of information between end-nodes is a key enabler for secure quantum networks and quantum secret key sharing, which rely on creating and sustaining entangled states over time. However, such pairwise entanglements degrade due to channel loss and the storage of the entangled photons at the network nodes. The state of entanglement in turn impacts fidelity, a metric which quantifies the degree of similarity between a pair of quantum states. In this paper, we propose a routing solution that satisfies threshold fidelity requirements imposed by a receiver on the quantum information received from multiple transmitter nodes. Our solution selects intermediate repeaters from a pool of such nodes within the network to maximize the sum-rate of quantum information transfer. To this extent, we first provide expressions for the fidelity loss between adjacent nodes as well as for the end-to-end quantum data rate. Then, we propose a novel two-stage routing solution that (i) identifies the k-shortest paths for each transmitter using fidelity as cost metric and (ii) (heuristically) assigns a path for each transmitter depending on whether the repeater nodes have a single or multiple available memory units. Simulation results demonstrate that our proposed fidelity-based routing solution satisfies a wide range of fidelity requirements [0.6-0.79] while maximizing the quantum information transfer rate, outperforming the existing distance- and hop-based routing approaches.
Efficient routing of information between end-nodes is a key enabler for secure quantum networks and quantum secret key sharing, which rely on creating and sustaining entangled states over time. However, such pairwise entanglements degrade due to channel loss and the storage of the entangled photons at the network nodes. The state of entanglement in turn impacts fidelity, a metric which quantifies the degree of similarity between a pair of quantum states. In this paper, we propose a routing solution that satisfies threshold fidelity requirements imposed by a receiver on the quantum information received from multiple transmitter nodes. Our solution selects intermediate repeaters from a pool of such nodes within the network to maximize the sum-rate of quantum information transfer. To this extent, we first provide expressions for the fidelity loss between adjacent nodes as well as for the end-to-end quantum data rate. Then, we propose a novel two-stage routing solution that (i) identifies the k-shortest paths for each transmitter using fidelity as cost metric and (ii) (heuristically) assigns a path for each transmitter depending on whether the repeater nodes have a single or multiple available memory units. Simulation results demonstrate that our proposed fidelity-based routing solution satisfies a wide range of fidelity requirements [0.6-0.79] while maximizing the quantum information transfer rate, outperforming the existing distance- and hop-based routing approaches.
This paper studies reliable teleportation of quantum bits (called qubits) in a quantum data network with multiple sources (S) and destinations (D) as well as repeaters. To teleport qubits for a SD pair reliably, not only an entanglement path for the SD pair, but also appropriate purification of the links along the path is required to ensure that the end-to-end (E2E) fidelity of the established entanglement connections is high enough.This is the first work on quantifying the E2E fidelity, and also using this E2E fidelity to determine critical links to achieve the most resource efficient purification. A novel approach called E2E Fidelity aware Routing and Purification (EFiRAP) is proposed to maximize network throughput, i.e., the number of entanglement connections among multiple SD pairs, with each connection having an E2E fidelity above a given required threshold. EFiRAP accomplishes this goal by first preparing multiple candidate entanglement paths and determining optimal purification schemes, and then selecting the final set of entanglement paths that can maximize network throughput under the given quantum resource constraints. Existing works only ensured the fidelity of individual links, rather than the E2E fidelity is above a given threshold. Extensive simulations show that the proposed EFiRAP can enhance network throughput by about 50% when compared with the state-of-the-art approach.
A fully-quantum network implies the creation of quantum entanglement between a given source node and some other destination node, with a number of quantum repeaters in between. This paper tackles the problem of quantum entanglement distribution by solving the routing problem over an infrastructure based on quantum repeaters and with a finite number of pairs of entangled qubits available in each link. The network model considers that link purification is available such that a nested purification protocol can be applied at each link to generate entangled qubits with higher fidelity than the original ones. A low-complexity multi-objective routing algorithm to find the shortest path between any two given nodes is proposed and assessed for random networks, using a fairly general path extension mechanism that can fit a large family of particular technological requirements. Different types of quantum protocols require different levels of fidelity for the entangled qubit pairs. For that reason, the proposed algorithm identifies the shortest path between two nodes that assures an end-to-end fidelity above a specified threshold. The minimum requirements for the end-to-end entanglement fidelity depend on the whole extension of the paths, and cannot be looked at as a local property of each link. Moreover, one needs to keep track not only of the shortest path, but also of longer paths holding more entangled qubits than the shorter paths in order to satisfy the fidelity criterion. Thus, standard single parameter shortest-path algorithms do not necessarily converge to the optimal solution. The problem of finding the best path in a network subject to multiple criteria (known as multi-objective routing) is, in general, an NP-hard problem due to the rapid growth of the number of stored paths. This work proposes a metric that identifies and discards paths that are objectively worse than others. By doing so, the time complexity of the proposed algorithm scales near-to-linearly with respect to the number of nodes in the network, showing that the shortest-path problem in quantum networks can be solved with a complexity very close to the one of the classical counterparts. That is analytically proved for the case where all the links of a path have the same fidelity (homogeneous model). The algorithm is also adapted to a particular type of path extension, where different links along a path can be purified to different degrees, asserting its flexibility and near-to-linearity even when heterogeneous fidelities along the sections of a path are considered.
The core function of quantum networks is to establish high-fidelity quantum entanglement for long-distance communication. However, the main challenge is to efficiently allocate resources under limited conditions, maximize throughput, satisfy end-to-end (E2E) fidelity requirements, and prevent quantum decoherence caused by inefficient routing algorithms. Current research focuses on optimizing either throughput or fidelity, with a lack of approaches that optimize both simultaneously; furthermore, existing algorithms suffer from high computational complexity. To tackle these challenges, this study proposes a Satisfying Fidelity Threshold Routing and Adaptive Purification Strategy (SFTRAP). SFTRAP maximizes throughput for each request by selecting multiple paths and dynamically choosing links for entanglement purification based on the current state of link resources, thus minimizing throughput loss while satisfying fidelity threshold. The strategy also adaptively adjusts the number of purification rounds according to the fidelity threshold, thereby optimizing the time required for deep purification and enhancing algorithmic efficiency. For multi-request scenarios, SFTRAP employs a priority sorting mechanism that takes into account both path cost and path freedom, which refines request scheduling and path selection to create more efficient request combinations, thus further boosting the overall network throughput. Simulation results indicate that SFTRAP surpasses state-of-the-art methods in terms of both throughput and algorithmic efficiency, highlighting its potential for optimizing resources in quantum networks.
How to efficiently distribute entanglement over large-scale quantum networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks where each link is characterized by a trade-off between the entanglement generation rate and fidelity. For such networks, we look at the two following problems: the one of finding the best path to connect any two given nodes, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. Two entanglement distribution models are considered: one where entangled qubits are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. The paper proposes of a quite general methodology that uses continuous fidelity curves (i.e., entanglement generation fidelity vs. rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the link models and networks considered, it is proven that the algorithm always converges to the optimal solution. It is also shown through simulation that the execution time grows polynomially with the number of network nodes (growing with a power between 1 and 1.4, depending on the network)
Quantum repeaters incorporating quantum memory play a pivotal role in mitigating loss in transmitted quantum information (photons) due to link attenuation over a long-distance quantum communication network. However, limited availability of available storage in such quantum repeaters and the impact on the time spent within the memory unit presents a trade-off between quantum information fidelity (a metric that quantifies the degree of similarity between a pair of quantum states) and qubit transmission rate. Thus, effective management of storage time for qubits becomes a key consideration in multi-hop quantum networks. To address these challenges, we propose Q-REACH, which leverages queuing theory in caching networks to tune qubit transmission rate while considering fidelity as the cost metric. Our contributions in this work include (i) utilizing a method of repetition that encodes and broadcasts multiple qubits through different quantum paths, (ii) analytically estimating the time spent by these emitted qubits as a function of the number of paths and repeaters, as well as memory units within a repeater, and (iii) formulating optimization problem that leverages this analysis to correct the transmitted logic qubit and select the optimum repetition rate at the transmitter.
Future quantum networks will enable the interconnection of multiple users distributed across vast geographic distances. Due to these large separations and limited physical resources, communication will often rely on multi-path routing strategies, where physical resources are distributed across channels of varying lengths and delivered to end users. Efficient long-distance quantum communication therefore requires optimizing the allocation of these resources across available paths. In this work, we introduce a performance-oriented approach to quantum network routing by extending the classical concept of Quality of Service (QoS) to the context of multi-path quantum resources distribution. Unlike prior models that consider entanglement generation or quantum memory coherence in isolation, we investigate the interplay between path assignment strategies, coherence time constraints, and quantum error correction (QEC), and how they jointly impact end-to-end communication fidelity. We analyze both unencoded and encoded transmissions over aggregated network paths, quantifying the effects of resource allocation on transmission success. Our findings show that fidelity cannot be optimized independently of memory lifetimes, and that while QEC can enhance performance under specific conditions, it also imposes additional constraints depending on network topology and path-length asymmetries. This work provides a foundation for developing QoS-aware quantum routing protocols that balance fidelity, throughput, and memory utilization -- key considerations for near-term quantum repeater networks.