Abstract We conduct a numerical investigation of fiber-based entanglement distribution over distances of up to 1600 km using a chain of processing-node quantum repeaters. We determine minimal hardware requirements while simultaneously optimizing over protocols for entanglement generation and entanglement purification, as well as over strategies for entanglement swapping. Notably, we discover that through an adequate choice of protocols the hardware improvement cost scales linearly with the distance covered. Our results highlight the crucial role of good protocol choices in significantly reducing hardware requirements, such as employing purification to meet high-fidelity targets and adopting a swap as soon as possible policy for faster rates. To carry out this analysis, we employ an extensive simulation framework implemented with NetSquid, a discrete-event-based quantum-network simulator, and a genetic-algorithm-based optimization methodology to determine minimal hardware requirements.
Abstract We conduct a numerical investigation of fiber-based entanglement distribution over distances of up to 1600 km using a chain of processing-node quantum repeaters. We determine minimal hardware requirements while simultaneously optimizing over protocols for entanglement generation and entanglement purification, as well as over strategies for entanglement swapping. Notably, we discover that through an adequate choice of protocols the hardware improvement cost scales linearly with the distance covered. Our results highlight the crucial role of good protocol choices in significantly reducing hardware requirements, such as employing purification to meet high-fidelity targets and adopting a swap as soon as possible policy for faster rates. To carry out this analysis, we employ an extensive simulation framework implemented with NetSquid, a discrete-event-based quantum-network simulator, and a genetic-algorithm-based optimization methodology to determine minimal hardware requirements.
Abstract We perform a numerical study of the distribution of entanglement on a real-world fiber grid connecting the German cities of Bonn and Berlin. The connection is realized using a chain of processing-node quantum repeaters spanning roughly 900 kilometers. Their placement is constrained by the fiber grid we consider, resulting in asymmetric links. We investigate how minimal hardware requirements depend on the target application, as well as on the number of repeaters in the chain. We find that requirements for blind quantum computing are markedly different than those for quantum key distribution, with the required coherence time being around two and a half times larger for the former. Further, we observe a trade-off regarding how target secret-key rates are achieved when using different numbers of repeaters: comparatively low-quality entangled states generated at a high rate are preferred for higher numbers of repeaters, whereas comparatively high-quality states generated at a lower rate are favored for lower numbers of repeaters. To obtain our results we employ an extensive simulation framework implemented using NetSquid, a discrete-event simulator for quantum networks. These are combined with an optimization methodology based on genetic algorithms to determine minimal hardware requirements.
Abstract Long-distance quantum communication via entanglement distribution is of great importance for the quantum internet. However, scaling up to such long distances has proved challenging due to the loss of photons, which grows exponentially with the distance covered. Quantum repeaters could in theory be used to extend the distances over which entanglement can be distributed, but in practice hardware quality is still lacking. Furthermore, it is generally not clear how an improvement in a certain repeater parameter, such as memory quality or attempt rate, impacts the overall network performance, rendering the path toward scalable quantum repeaters unclear. In this work we propose a methodology based on genetic algorithms and simulations of quantum repeater chains for optimization of entanglement generation and distribution. By applying it to simulations of several different repeater chains, including real-world fiber topology, we demonstrate that it can be used to answer questions such as what are the minimum viable quantum repeaters satisfying given network performance benchmarks. This methodology constitutes an invaluable tool for the development of a blueprint for a pan-European quantum internet. We have made our code, in the form of NetSquid simulations and the smart-stopos optimization tool, freely available for use either locally or on high-performance computing centers.
Abstract We numerically study the distribution of entanglement between the Dutch cities of Delft and Eindhoven realized with a processing-node quantum repeater and determine minimal hardware requirements for verifiable blind quantum computation using color centers and trapped ions. Our results are obtained considering restrictions imposed by a real-world fiber grid and using detailed hardware-specific models. By comparing our results to those we would obtain in idealized settings, we show that simplifications lead to a distorted picture of hardware demands, particularly on memory coherence and photon collection. We develop general machinery suitable for studying arbitrary processing-node repeater chains using NetSquid, a discrete-event simulator for quantum networks. This enables us to include time-dependent noise models and simulate repeater protocols with cut-offs, including the required classical control communication. We find minimal hardware requirements by solving an optimization problem using genetic algorithms on a high-performance-computing cluster. Our work provides guidance for further experimental progress, and showcases limitations of studying quantum-repeater requirements in idealized situations.
Abstract We address the problem of efficiently distributing high-fidelity entangled states across the nodes of a quantum network—a fundamental requirement for quantum communication, distributed quantum computing, and emerging quantum internet applications. We consider a repeater-based architecture that combines entanglement swapping (or fusion) with purification operations, which enhance fidelity by consuming additional entangled pairs. While prior work has explored routing and limited purification strategies, we present the first algorithms for fidelity-constrained entanglement distribution that are near-optimal and compatible with arbitrary purification models. Our approach introduces the notion of purification-augmented entanglement trees, and we develop dynamic programming (DP) algorithms to construct such trees that maximize the generation rate of entangled pairs (EPs) under fidelity constraints. We further extend our framework to a linear programming (LP)–based flow model that enables simultaneous generation of EPs across multiple source-destination pairs. For multipartite entanglement, we generalize our methods to GHZ and arbitrary graph states, supported by novel analytical models for fidelity evolution under fusion and purification. We evaluate our techniques using the NetSquid quantum network simulator and observe consistent performance improvements over prior approaches—achieving an average 50\% increase in generation rate, and up to 100-150\% in some scenarios.
A large scale quantum network requires the distribution of high-fidelity end-to-end entanglement. To overcome the range limitations inherent to terrestrial fiber, a leading architecture has emerged: satellite-based sources transmitting entanglement to quantum repeaters on the ground. By bridging the gap between abstract analytical frameworks and computationally heavy numerical simulations, this paper provides the first quantitative answer to the question of such a network's achievable performance with current and near-term space technology, while accounting for entanglement swapping and purification. This is achieved by integrating a detailed physical model of a satellite-to-ground link into an analytical entanglement resource estimation framework for quantum repeaters, enabling an optimization of the end-to-end entanglement rate. Our analysis, performed across leading quantum hardware platforms, shows that Low Earth Orbit satellite constellations combined with quantum repeaters employing Neutral Atom or Nitrogen and Silicon Vacancy qubits, could enable a global quantum network, distributing entanglement over distances up to 20,000 km, sufficient for connecting any two points on Earth. This work highlights the major bottlenecks in space and quantum hardware technologies, which need to be addressed, thereby guiding informed investments necessary for enabling a large scale quantum network.
Long-distance quantum communication requires reliable entanglement distribution, but direct generation with protocols such as Barrett--Kok suffers from exponentially decreasing success probability with distance, making it impractical over hundreds of kilometers. Quantum repeaters address this by segmenting the channel and combining entanglement generation, swapping, and purification. In this work, we present a simulation framework for chain-based repeaters under continuous-time depolarizing noise. Our model implements heralded entanglement generation, Bell-state swapping, and multi-round purification, with configurable chain length, noise levels, and purification depth. Numerical results highlight how memory decoherence constrains performance, how purification mitigates fidelity loss, and how time and entanglement costs scale with distance. While simplified, the framework offers a flexible tool for exploring trade-offs in repeater design and provides a basis for extensions toward more complex network scenarios.