We consider scheduling in a quantum switch with stochastic entanglement generation, finite quantum memories, and decoherence. The objective is to design a scheduling algorithm with polynomial-time computational complexity that stabilizes a nontrivial fraction of the capacity region. Scheduling in such a switch corresponds to finding a matching in a graph subject to additional constraints. We propose an LP-based policy, which finds a point in the matching polytope, which is further implemented using a randomized decomposition into matchings. The main challenge is that service over an edge is feasible only when entanglement is simultaneously available at both endpoint memories, so the effective service rates depend on the steady-state availability induced by the scheduling rule. To address this, we introduce a single-node reference Markov chain and derive lower bounds on achievable service rates in terms of the steady-state nonemptiness probabilities. We then use a Lyapunov drift argument to show that, whenever the request arrival rates lie within the resulting throughput region, the proposed algorithm stabilizes the request queues. We further analyze how the achievable throughput depends on entanglement generation rates, decoherence probabilities, and buffer sizes, and show that the throughput lower bound converges exponentially fast to its infinite-buffer limit as the memory size increases. Numerical results illustrate that the guaranteed throughput fraction is substantial for parameter regimes relevant to near-term quantum networking systems.

翻译：我们研究具有随机纠缠生成、有限量子存储器和退相干的量子交换机中的调度问题。目标是设计一种具有多项式时间计算复杂度的调度算法，该算法能够稳定容量区域的非平凡部分。此类交换机中的调度对应于在具有额外约束的图中寻找匹配。我们提出了一种基于线性规划的策略，该策略找到匹配多面体中的一个点，然后通过随机分解为多个匹配来实现。主要挑战在于，只有当纠缠同时存在于两个端点存储器中时，通过一条边的服务才是可行的，因此有效服务速率取决于由调度规则决定的稳态可用性。为了解决这个问题，我们引入了一个单节点参考马尔可夫链，并根据稳态非空概率推导了可实现服务速率的下界。然后，我们使用李雅普诺夫漂移论证表明，只要请求到达率位于由此产生的吞吐量区域内，所提出的算法就能稳定请求队列。我们进一步分析了可实现吞吐量如何依赖于纠缠生成速率、退相干概率和缓冲区大小，并表明随着存储器大小的增加，吞吐量下界以指数速度收敛到其无限缓冲区极限。数值结果表明，对于与近期量子网络系统相关的参数范围，保证的吞吐量比例是显著的。