量子中继链中的最优纠缠路由：超越固定操作顺序与纯化调度
Optimal Entanglement Routing in Quantum Repeater Chains: Beyond Fixed Operation Order and Purification Schedule
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中文总结 AI 辅助
本研究针对量子中继链纠缠路由，提出统一优化框架，证明纯化调度（树形优于泵浦）是决定可行性的主导因素，而操作顺序为替代因素。
中文摘要 AI 辅助
纠缠路由通过纯化和交换在基本链路上生成的纠缠对，在量子网络的远距离节点之间建立纠缠对。现有方法通常沿两个轴限制决策空间：操作顺序（通常固定为先纯化后交换，即PtS）以及每条链路的纯化调度（通常限制为泵浦方式）。我们关注具有有限链路容量的线性中继链，放宽了这两个限制，并在两种量子噪声模型下研究在满足保真度阈值条件下最大化期望端到端吞吐量的问题。我们开发了一个统一的自感知容量优化框架，包含在PtS下的精确混合整数线性规划（MILP），可实例化为泵浦或通用树形纯化调度，以及一个在任意操作顺序下的精确动态规划（DP）。在对称泡利噪声下，我们证明泵浦方式收敛到的保真度严格低于1，这给所有基于泵浦的PtS方法施加了一个与容量无关的可行性界限和最大链长，而通用树形调度则产生依赖于容量的界限。我们进一步证明，交换后纯化永远不会提高吞吐量，因此自由操作顺序只能增加可行性。数值评估证实了这些界限：在中等保真度阈值下，树形调度可服务超过90%的泵浦方式无法服务的请求；在泵浦类别内，自由操作顺序恢复了这一优势的很大一部分；但一旦链路使用树形调度，基于树的MILP和顺序精确DP在整个过程中服务相同的请求集。因此，操作顺序和纯化调度是可替代的，其中纯化调度是在对称泡利噪声下控制可行性的主导因素。
英文摘要
Entanglement routing establishes entangled pairs between distant nodes of a quantum network by purifying and swapping pairs generated on elementary links. Existing methods typically restrict the decision space along two axes: the operation order, often fixed to purify-then-swap (PtS), and the purification schedule of each link, often restricted to pumping. Focusing on linear repeater chains with finite link capacities, we relax both restrictions and study the maximization of the expected end-to-end throughput subject to a fidelity threshold under two quantum-noise models. We develop a unified capacity-aware optimization framework comprising an exact mixed-integer linear program (MILP) under PtS, instantiated with either pumping or general tree purification schedules, and an exact dynamic program (DP) over arbitrary operation orders. Under symmetric Pauli noise, we prove that pumping converges to a fidelity strictly below unity, imposing a capacity-independent feasibility bound and a maximum chain length on every pumping-based PtS method, whereas general tree schedules yield a capacity-dependent bound. We further prove that post-swap purification never increases the throughput, so a free operation order can only increase feasibility. Numerical evaluations confirm the bounds: tree schedules serve over 90\% of the requests that pumping cannot at moderate fidelity thresholds; within the pumping class, a free operation order recovers much of this advantage; but once links use tree schedules, the tree-based MILP and the order-exact DP serve identical request sets throughout. Operation order and purification schedule are thus substitutes, with the purification schedule the dominant factor governing feasibility under symmetric Pauli noise.
发表机构
- National and Kapodistrian University of Athens（雅典国立卡波第斯特里安大学）
- Eulambia Advanced Technologies Ltd.（尤兰比亚先进技术有限公司）
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