AI summaryⓘ
The authors study a quantum switch that uses a limited number of memory slots to help several users share special quantum connections called entanglements. They design rules for how the switch should decide which user requests to handle to serve as many requests as possible over time. To evaluate these rules, they use a new measure called the age of entanglement establishment, which tracks how fresh the connections are. They mathematically model the problem using a tool called restless multi-armed bandits and find formulas (Whittle indices) that help them decide which requests to prioritize. Finally, they turn the scheduling into a known optimization problem (knapsack) and propose simpler methods based on these indices for easier computation.
quantum switchmultipartite entanglementquantum memory registersage of entanglement establishmentrestless multi-armed banditWhittle index0-1 knapsack problemdynamic programmingscheduling policy
Authors
Subhankar Banerjee, Stavros Mitrolaris, Sennur Ulukus
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.