Index-Based Scheduling for a Resource-Constrained Quantum Switch

Abstract

We consider a quantum switch with a finite number of quantum memory registers that aims to serve multipartite entanglement requests among $N$ users. We propose scheduling policies that aim to optimize the average number of requests served per unit time by efficiently utilizing the switch's available memory. To measure the performance of the scheduling policies, we employ the newly introduced metric of age of entanglement establishment (AoEE). We formulate the scheduling problem in a restless multi-armed bandit (RMAB) framework. We show that the scheduling of entanglement requests is indexable. Subsequently, we find a closed-form expression of the Whittle index for all possible request-age pairs. By modeling the Whittle index of each request as its reward and its cardinality as its cost, we formulate the memory-constrained scheduling problem as a $0$-$1$ knapsack problem and solve it via dynamic programming. Furthermore, we consider two low-complexity sequential greedy policies that leverage two different modified Whittle indices.

Figures (4)

• Figure 1: An illustrative example of an entanglement swapping operation. In (a), the switch has established LLEs with two users and stores the corresponding qubits in the memory. In (b), the switch performs a Bell-state measurement on the locally stored qubits. In (c), end-to-end entanglement between the users has been established.
• Figure 2: Example with $R=4$ requests, with $|\mathcal{G}(1)|=2, |\mathcal{G}(2)|=2$, $|\mathcal{G}(3)|=3$, and $|\mathcal{G}(4)|=4$. The requests are represented by the colors green, blue, orange, and pink, respectively. The top figure shows the evolution of the age of entanglement establishment for request $1$ (green) under policy $\pi$, and the bottom figure shows the corresponding memory-register allocation with $M=5$ memory registers. At time $t$, a memory block allocated to a request is shown using a lighter shade of the corresponding color, while a successfully established LLE for that request is shown using the darker shade. For example, at time slot $1$, request $4$ (pink) is scheduled, and the first four blocks are allocated to it; however, only three users in the request successfully establish LLEs.
• Figure 3: Average age of entanglement establishment achieved by the proposed policies of this work and of mitrolaris2026age as a function of the memory size $M$ in a network with $N=5$ users and all possible requests, $R=2^N-(N+1)=26$.
• Figure 4: Average age of entanglement establishment achieved by the proposed policies of this work and of mitrolaris2026age as $\mathcal{R}$ expands in a network with $N=7$ users and $M=20$.

Theorems & Definitions (4)

• Theorem 1
• Theorem 2
• Lemma 1
• Lemma 2