The Quantum Internet will allow clients to delegate quantum workloads to remote servers over heterogeneous networks, but choosing the server that minimizes end-to-end execution time is difficult because server processing, feedforward classical communication, and entanglement distribution can overlap in protocol-dependent ways and shift the runtime bottleneck. We propose $T_{\max}$, a lightweight runtime score that sums coarse telemetry from multiple layers to obtain a conservative ranking for online server selection without calibrating weights for each deployment. Using NetSquid discrete-event simulations of a modified parameter-blind VQE (PB-VQE) workload, we evaluate $T_{\max}$ on pools of 10,000 heterogeneous candidates (selecting among up to 100 per decision) across crossover and bottleneck-dominated regimes, including temporal jitter scenarios and jobs with multiple shots. $T_{\max}$ achieves single-digit mean regret normalized by the oracle (below 10%) in both regimes and remains in the single-digit range under classical communication latency jitter for multi-shot jobs, while performance degrades for single-shot jobs under severe jitter. To connect performance to deployment planning, we derive an operating map based on requirements relating distance and entanglement rate requirements to protocol level counts, quantify how simple multiuser contention shifts the crossover, and use Sobol global sensitivity analysis to identify regime-dependent bottlenecks. These findings suggest that simple cross-layer telemetry can enable practical server selection while providing actionable provisioning guidance for emerging Quantum Internet services.

翻译：量子互联网将允许客户端通过异构网络将量子工作负载委托给远程服务器，但选择能够最小化端到端执行时间的服务器是困难的，因为服务器处理、前馈经典通信和纠缠分布可能以协议相关的方式重叠，从而改变运行时的瓶颈。我们提出$T_{\max}$，一种轻量级运行时评分方法，它汇总来自多个层的粗略遥测数据，以获得一个保守的排名，用于在线服务器选择，而无需为每个部署校准权重。使用改进的参数盲变分量子本征求解器（PB-VQE）工作负载的NetSquid离散事件模拟，我们在交叉和瓶颈主导的两种机制下，对包含10,000个异构候选服务器的池（每次决策最多选择100个）评估了$T_{\max}$，评估场景包括时间抖动和多轮次作业。$T_{\max}$在两种机制下均实现了相对于最优解的个位数平均归一化遗憾（低于10%），并且在多轮次作业面临经典通信延迟抖动时，遗憾值仍保持在个位数范围，而在严重抖动下，单轮次作业的性能会下降。为了将性能与部署规划联系起来，我们推导了一个基于距离和纠缠率要求与协议层数关系的需求操作图，量化了简单的多用户竞争如何改变交叉点，并使用Sobol全局敏感性分析来识别机制相关的瓶颈。这些发现表明，简单的跨层遥测可以实现实用的服务器选择，同时为新兴的量子互联网服务提供可操作的资源配置指导。