LP-Based Algorithms for Scheduling in a Quantum Switch

2026-03-29

AI Summary

This work addresses the scheduling challenge in quantum switches arising from stochastic entanglement generation, limited quantum memory, and decoherence. The problem is formulated as a constrained graph matching task, and a linear programming–based scheduling strategy is proposed: feasible schedules are obtained by selecting a point within the matching polytope and applying randomized decomposition. A novel single-node reference Markov chain is introduced to derive a lower bound on the service rate, and system stability is established via Lyapunov drift analysis. The study further demonstrates that throughput converges exponentially to the infinite-buffer limit as memory capacity increases. The algorithm operates in polynomial time and achieves substantial throughput under typical quantum network parameters, with its performance lower bound rapidly improving as memory size grows.

Abstract

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.

Problem

• quantum switch
• scheduling
• entanglement generation
• decoherence
• throughput

Innovation

• LP-based scheduling
• quantum switch
• matching polytope
• Lyapunov drift analysis
• entanglement availability