LP-Based Algorithms for Scheduling in a Quantum Switch

TL;DR

This paper develops an LP-based scheduling algorithm for quantum switches with stochastic entanglement, finite memories, and decoherence, ensuring stability within a significant capacity region.

Contribution

It introduces a polynomial-time LP-based policy that stabilizes request queues in quantum switches considering physical constraints and steady-state availability.

Findings

The algorithm stabilizes queues when request rates are within the derived throughput region.

Throughput lower bounds depend on entanglement rates, decoherence, and buffer sizes.

The throughput lower bound converges exponentially fast to the infinite-buffer limit as memory size increases.

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.