Age-Based Scheduling for a Memory-Constrained Quantum Switch

TL;DR

This paper tackles scheduling multipartite entanglement requests in a memory-constrained quantum switch by introducing a novel QoS metric, the age of entanglement establishment (AoEE). It develops three low-complexity policy families—single-cardinality stationary randomized (SSR), single-cardinality max-weight (SMW), and multi-cardinality max-age (MMA)—and derives closed-form AoEE expressions and performance guarantees for them. SSR yields a tractable closed-form for average AoEE and an optimal policy via marginal probabilities; SMW improves upon SSR using a max-weight approach with a formal bound showing $\,\Delta^{\bm\psi} \le \Delta^{\bm\mu^*}$. MMA extends to multiple maximal feasible cardinality subsets and uses a convex optimization to choose a sampling distribution, with a detailed AoEE expression and scheduling rule. Numerical results illustrate memory-size effects and the trade-offs among policies, highlighting practical, linear-time implementable strategies as baselines for memory-limited quantum-switch scheduling.

Abstract

In a time-slotted system, we study the problem of scheduling multipartite entanglement requests in a quantum switch with a finite number of quantum memory registers. Specifically, we consider probabilistic link-level entanglement (LLE) generation for each user, probabilistic entanglement swapping, and one-slot decoherence. To evaluate the performance of the proposed scheduling policies, we introduce a novel age-based metric, coined age of entanglement establishment (AoEE). We consider two families of low-complexity policies for which we obtain closed-form expressions for their corresponding AoEE performance. Optimizing over each family, we obtain two policies. Further, we propose one more low-complexity policy and provide its performance guarantee. Finally, we numerically compare the performance of the proposed policies.

Figures (3)

• Figure 1: An illustrative example of an entanglement swapping operation. In (a), the quantum switch is connected to four users, and no LLEs have been established. In (b), the switch establishes LLEs with two users and stores the corresponding qubits in the memory. In (c), by performing local operations on the stored qubits, the switch creates an end-to-end entangled pair between the two users.
• Figure 2: Average AoEE achieved by the proposed policies as a function of the memory size $M$ in a network with $N=5$ users and all possible requests, $|\mathcal{R}|=2^N-(N+1)=26$.
• Figure 3: Average AoEE achieved by the proposed policies as the set of requests expands in a network with $N=7$ users and $M=20$. Starting from all bipartite requests, we progressively include all requests of larger cardinalities until all possible requests are present.

Theorems & Definitions (8)

• Definition 1
• Lemma 1
• Theorem 1
• Definition 2
• Theorem 2
• Definition 3
• Lemma 2
• Proposition 1