quantum network operators

Abstract: Large-scale Quantum Key Distribution (QKD) networks rely on trusted repeaters, making the security properties of the selected communication path an essential part of end-to-end assurance. At the same time, network operators may be unwilling to disclose their internal topology. We present a topology-certification mechanism that lets a provider prove in zero knowledge that policy-compliant routes between two endpoints exist, without disclosing the routes in an individual presentation. Our main idea is to certify nodes and edges independently using multi-message signatures, rather than signing the complete graph as one object. For a route chosen in advance, proof size and cryptographic proving and verification work depend on its positions and attributes, independently of the overall network size, whereas route discovery and certification have separate graph-dependent costs. The construction hides the actual route length up to a public bound and sketches extensions to node-disjoint routes and monotonic additions within a graph epoch. We give a formal security model and conditional proofs of unforgeability and graph hiding for a generic construction. For a BBS-based construction, presentation-size estimates remain below $300$\,KiB at $\ell=m=n=50$, and measured generation and verification times remain below $400$\,ms at $\ell=64$ and $m=n=8$.

Abstract: Emerging experimental quantum network deployments are based on collaborations between research institutions and rely on telecommunications fiber infrastructure. Currently, such networks consist of mostly Dual Input Repeaters (DIRs) and can be viewed as composed of (mostly) line graphs. In order to evaluate the performance of such networks (e.g., in terms of Entangled Pair Rate, EPR, and average Fidelity) we developed a custom quantum network simulation platform that takes into account both the quantum and classical network components. To support the verification of the simulation results, we develop a novel approach for performance analysis of DIRs. We compare the simulation results to the analytical results for DIRs and to prior results for repeaters with more than two inputs. We observe that although the expected memory utilization cannot be bounded, \emph{a small DIR memory size is sufficient and leads to minimal performance degradation}. For line networks with a single repeater and $3$ repeaters, we explore the dependency of incoming and outgoing memory size requirements on the number of nodes (network size), their connectivity (fiber length) and various quantum error settings (amplitude damping and phase flip channels). We evaluate the \emph{EPR} and the \emph{average Fidelity} for a sub-network of a deployed network with $3$ repeaters, using two alternative paths. We show that as the number of nodes increases or when the fiber lengths between nodes differ significantly, additional node memory is needed to maintain the same EPR (qubits are stored for longer duration to allow completion of entanglement across the network). We also show that the memory size should be above some minimum threshold to allow EP creation (EPR $>0$) as pair selection and swapping completion propagate across the network.

Abstract: Future quantum networks will make use of entanglement to perform numerous tasks, such as sending quantum information over long distances, distributed quantum computing, and quantum sensing. In general, these tasks will need to be performed simultaneously in various regions of a network, while minimizing resources and latency. We will thus require policies for scheduling link-level entanglement resources, and using the link-level entanglement to create various forms of multipartite entanglement required for every task. In this work, we address this problem using reinforcement learning. We formulate a Markov Decision Process for the problem and use double deep Q-networks (DQN) with Message Passing Neural Networks (MPNNs), experience replay buffers, and curriculum training to obtain policies. The key physical parameter is the probability of link-level entanglement generation, i.e., the link activation probability. We show that our policies maintain 100% success for up to 71% lower link activation probability than the baseline heuristics for a set of physically relevant network topologies. We then examine an additional constraint where experiment (task) placements are restricted to specific hardware types and demonstrate a similar advantage in performance over heuristics, with our policy maintaining at least an 80% success rate for up to a 59% lower link activation probability. Finally, we explore methods to interpret the learned policy by defining metrics enabling conclusions to be drawn about the model's behavior and by tasking a large language model (LLM) to derive a novel heuristic given example actions taken by the DQN-trained policy. We find that the LLM heuristic performs similarly to the DQN-trained policy in performance, indicating a promising method for interpretable policy extraction for large quantum networks, where direct training becomes computationally expensive.

Abstract: In quantum networks, nodes are connected via sharing of Einstein-Podolsky-Rosen (EPR) pairs, ideally with high fidelity and high rate. However, the fidelity of EPR pairs degrades due to imperfect generation and decoherence errors. Entanglement Distillation is a method that increases the fidelity but operates probabilistically and may destroy all involved EPR pairs upon failure. This failure reduces available EPR pairs for application use, thereby decreasing the service rate. Quantum Error Correction (QEC) is another mechanism to protect EPR pairs against error by forming what we term as Coding-Enhanced Memory (CEM). While effective, CEM requires extra time and resources to form the code, which also reduces the service rate. Existing methods often use static combinations of distillation and CEM, ignoring demand variations. This results in a low service rate without significant fidelity gain. Limited resources together with this rate-fidelity tradeoff make it essential to schedule when to run distillation, form CEM, or serve requests. We propose ReFINE, a demand-aware preemptive scheduler that based on application requirements either serves an available EPR pair immediately or preserves it in CEM. This selective use of CEM, only when needed, enables a better balance for rate-fidelity tradeoff than always using CEM. Between request arrivals, ReFINE either schedules distilling EPR pairs or forming CEM to protect distilled pairs, following one of the three priority policies: ReFINE-D (Distillation-First) first generates EPR pairs for distillation and then forms the CEM, prioritizing service rate. ReFINE-M (Memory-First) first forms the CEM, then generates the EPR pairs for distillation, prioritizing fidelity. ReFINE-C (Concurrent) performs both distillation and CEM formation concurrently, balancing between fidelity and service rate.

Abstract: 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.