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Entropy

Many-Objective Optimisation of Global Quantum Internet Topologies: A Compact Parametric Representation with an Analytical BDCZ Oracle

Jesús Gil Ruiz, Diego Rodríguez Rodríguez, Rafael Muñoz Gil

Published Sep 21, 2026• 0 citations
Publisher

Abstract

We address the design of global quantum internet topologies that jointly optimise four physical objectives: average end-to-end Werner-state fidelity, entanglement rate, latency and coverage, evaluated with an analytical BDCZ oracle whose path selection is exact under the stated Werner-composition model and whose satellite links respect a single-satellite visibility limit. The search space is heterogeneous (fibre, satellite, free-space optical), comprising 1002=4950 possible edges over 100 cities; direct per-edge categorical optimisation degenerates. We propose a mixed representation of ten physical design parameters plus one stochastic realisation index (eleven decision variables in total) decoding into a topology via k-nearest-neighbour rules. Seven many-objective algorithms (NSGA-II, NSGA-III, MOEA/D, SMS-EMOA, RVEA, SPEA2, AGE-MOEA-II) are compared at a matched budget over 30 seeds, scored against a shared reference front. NSGA-II attains the highest mean hypervolume (0.353±0.040) but is statistically indistinguishable from SPEA2 and AGE-MOEA-II (0.352, 0.347); after Holm correction across all 63 tests, this top group separates significantly from NSGA-III, SMS-EMOA, RVEA and MOEA/D, though NSGA-III and SMS-EMOA remain indistinguishable in HV/IGD (spacing unresolved). NSGA-II’s lead is driven by 6 of its 30 seeds reaching a higher-HV region, a bimodality we report. An eight-variant decoder ablation (NSGA-III) shows fibre is necessary while satellite’s contribution is not detectable, and one classical constructor (a Random Geometric Graph) remains non-dominated; none of the 561 front points connects all 100 cities under the satellite model. On four additional real-city instances (five algorithms), MOEA/D is last throughout; SMS-EMOA/RVEA ranks vary by instance, and NSGA-II/NSGA-III reverses, without significance, twice; the fibre transmittance law is cross-checked against SeQUeNCe (Spearman ρ=1.0). The pooled front is released as QI-Bench-Pareto-v1.

DOI
10.3390/e28091041

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We address the design of global quantum internet topologies that jointly optimise four physical objectives: average end-to-end Werner-state fidelity, entanglement rate, latency and coverage, evaluated with an analytical BDCZ oracle whose path selection is exact under the stated Werner-composition model and whose satellite links respect a single-satellite visibility limit. The search space is heterogeneous (fibre, satellite, free-space optical), comprising 1002=4950 possible edges over 100 cities; direct per-edge categorical optimisation degenerates. We propose a mixed representation of ten physical design parameters plus one stochastic realisation index (eleven decision variables in total) decoding into a topology via k-nearest-neighbour rules. Seven many-objective algorithms (NSGA-II, NSGA-III, MOEA/D, SMS-EMOA, RVEA, SPEA2, AGE-MOEA-II) are compared at a matched budget over 30 seeds, scored against a shared reference front. NSGA-II attains the highest mean hypervolume (0.353±0.040) but is statistically indistinguishable from SPEA2 and AGE-MOEA-II (0.352, 0.347); after Holm correction across all 63 tests, this top group separates significantly from NSGA-III, SMS-EMOA, RVEA and MOEA/D, though NSGA-III and SMS-EMOA remain indistinguishable in HV/IGD (spacing unresolved). NSGA-II’s lead is driven by 6 of its 30 seeds reaching a higher-HV region, a bimodality we report. An eight-variant decoder ablation (NSGA-III) shows fibre is necessary while satellite’s contribution is not detectable, and one classical constructor (a Random Geometric Graph) remains non-dominated; none of the 561 front points connects all 100 cities under the satellite model. On four additional real-city instances (five algorithms), MOEA/D is last throughout; SMS-EMOA/RVEA ranks vary by instance, and NSGA-II/NSGA-III reverses, without significance, twice; the fibre transmittance law is cross-checked against SeQUeNCe (Spearman ρ=1.0). The pooled front is released as QI-Bench-Pareto-v1.
The development of a future, global quantum communication network (or quantum internet) will enable high rate private communication and entanglement distribution over very long distances. However, the large-scale performance of ground-based quantum networks (which employ photons as information carriers through optical-fibres) is fundamentally limited by the fibre quality and link length. While these fundamental limits are well established for arbitrary network architectures, the question of how to best design these global architectures remains open. In this work, we take a step forward in addressing this problem by modelling global quantum networks with weakly-regular architectures. Such networks are capable of idealising end-to-end performance whilst remaining sufficiently realistic. In this way, we may investigate the effectiveness of large-scale networks with consistent connective properties, and unveil the global conditions under which end-to-end rates remain analytically computable. Furthermore, by comparing the performance of ideal, ground-based quantum networks with satellite quantum communication protocols, we can establish conditions for which satellites can be used to outperform fibre-based quantum infrastructure.
The design and operation of quantum networks are both decisive in the current push towards a global quantum internet. Although space-enabled quantum connectivity has already been identified as a beneficial candidate for long-range quantum channels for over two decades, the architecture of a hybrid space-ground network is still a work in progress. Here, we propose an analysis of such a network based on a best-path approach, where either fiber- or satellite-based elementary links can be concatenated to form a repeater chain. The network consisting of quantum information processing nodes, equipped with both ground and space connections, is mapped into a graph structure, where edge weights represent the achievable secret key rates, chosen as the figure of merit for the network analysis. A weight minimization algorithm allows identifying the best path dynamically, i.e., as the weather conditions, stray light radiance, and satellite orbital position changes. From the results we conclude that satellite links will play a significant role on the future large-scale quantum internet, and both a constellation of satellites and significant advances in filtering technology are required to fulfill continuous coverage.
Hybrid terrestrial-satellite quantum networks combine terrestrial fiber infrastructure with free-space links to enable long-distance entanglement distribution. Entanglement can be routed over different combinations of terrestrial and satellite links, resulting in paths with different entanglement generation rates (EGRs) and fidelities. Existing routing algorithms, however, typically reduce routing to a single-objective problem by optimizing either EGR or fidelity, or by optimizing one while constraining the other, and thus do not explicitly capture the trade-off between the two. In this paper, we present a bi-objective routing framework for hybrid quantum networks that jointly optimizes end-to-end EGR and fidelity. We formulate routing as a Pareto optimization problem and show that it possesses a special mathematical structure: the bottleneck nature of end-to-end EGR and the multiplicative nature of end-to-end fidelity allow the problem to be transformed into a MAXMIN-MINSUM bi-criterion path problem. This transformation enables the exact polynomial-time computation of a minimal complete Pareto set using Martins' bicriterion routing algorithm. Our results demonstrate that hybrid networks expose substantially richer Pareto frontiers than terrestrial-only networks and that the proposed framework outperforms representative single-objective routing policies by allowing applications to select paths based on their EGR and fidelity requirements.
Quantum networks are usually framed by two hardware limits: how fast entanglement can be heralded, and how long a memory can hold it. We establish a third, geometric limit: entanglement decoheres while control information travels, so the distance to whoever allocates resources enters the fidelity budget directly. We develop a functional-graph abstraction weighting each link by its predicted multiplicative contribution to end-to-end fidelity, separating global but delayed state from local and immediate state, and compare centralized against local allocation in a replicated discrete-event model. Centralized delivery latency grows with network diameter while local latency is nearly scale invariant, differing up to twenty-fold for short-range traffic; the coherence threshold at which a global view outweighs a fresh one does not shift across the tested sizes; and as heralding accelerates, the dominant cost moves into the control plane. Slot synchronization instead obeys the product of slot rate and one-way link delay, so it is bounded by repeater spacing rather than diameter. Controller placement, decision locality, repeater spacing and slot rate are physical design parameters, not implementation details.
Satellite optical links may be able to extend quantum communication range beyond that which is possible through optical fibres which are constrained by exponential loss scaling. Quantum repeaters have been proposed to mitigate high channel losses in both fibre and satellite links. Although satellite quantum repeaters could improve entanglement distribution efficiency, the attempt rate is constrained by classical communication latency in the entanglement swapping step. Direct entanglement distribution does not suffer this latency and can therefore compensate for high dual-downlink losses by increasing the source rate. A systematic comparative analysis of repeater-assisted and direct entanglement distribution rates using a satellite is absent from the literature. In addition to entanglement distribution rates, a detailed analysis of the fidelity of entanglement distributed by repeater-assisted satellite links has yet to be performed. Here, we develop an in-depth framework for describing a space quantum link consisting of a single satellite and two ground stations. We compare the entanglement distribution rates of direct and repeater-assisted satellite entanglement distribution, taking into account variations in overpass geometry and quantum memory capacity. The long-term entanglement distribution performance to different pairs of major cities is also considered, and the altitudinal dependence is explored. Furthermore, we develop a Monte Carlo model of the repeater satellite to explore the effect that different memory management policies and capacities have on the waiting time statistics of memory qubits. From these statistics we calculate the fidelity distributions of the entangled pairs established between the ground stations. These results will inform mission design for future space-borne quantum repeater nodes, as well as requirements on space-based memory platforms.
Quantum cloud platforms need to dynamically orchestrate workloads across heterogeneous quantum computation backends whose noise profiles, qubit topologies, and queues vary over time. Existing orchestrators use noise-agnostic heuristics that ignore backend-specific errors, causing reduced execution fidelity, load imbalance, and frequent rescheduling. To address these challenges, we propose QCOEM - a Quantum Cloud Orchestration framework that leverages Evolutionary algorithms for Multi-objective optimization of quantum task scheduling. We compare NSGA-II and NSGA-III for jointly minimizing mean completion time, execution error rate, and load imbalance. To select schedules from a non-convex Pareto front, we apply an Augmented Achievement Scalarization Function (AASF) as a preference-based decision rule that maps the Pareto set to a single dispatchable schedule aligned with user priorities. Our extensive performance evaluation in a heterogeneous quantum cloud environment shows zero task rescheduling and about 30% higher mean fidelity than noise-agnostic heuristics, while maintaining bounded scheduling overhead. The experiment results indicate that our QCOEM framework can deliver stable, high-fidelity execution and lightweight resource management for quantum cloud computing.