Service-the-Longest-Queue Among d Choices Policy for Quantum Entanglement Switching

TL;DR

This work addresses efficient entanglement distribution in quantum networks by studying an Entanglement Generation Switch (EGS) within a star topology. It proposes a $d$-choices load-balancing policy where the EGS samples $d$ node-queues and services the longest, augmented by a back-off mechanism to reduce classical communication overhead; the analysis relies on a mean-field limit to capture system dynamics. The authors derive mean-field differential equations, prove the existence and uniqueness of the equilibrium, and provide expressions for queue-size distributions and average response times, supported by numerical simulations. The results show a substantial reduction in waiting time when increasing from $d=1$ to $d=2$, with diminishing returns for larger $d$, and indicate that the mean-field model accurately approximates moderate-sized systems, offering practical guidance for near-term quantum-switch design and highlighting avenues for stability analysis and topology extensions.

Abstract

An Entanglement Generation Switch (EGS) is a quantum network hub that provides entangled states to a set of connected nodes by enabling them to share a limited number of hub resources. As entanglement requests arrive, they join dedicated queues corresponding to the nodes from which they originate. We propose a load-balancing policy wherein the EGS queries nodes for entanglement requests by randomly sampling d of all available request queues and choosing the longest of these to service. This policy is an instance of the well-known power-of-d-choices paradigm previously introduced for classical systems such as data-centers. In contrast to previous models, however, we place queues at nodes instead of directly at the EGS, which offers some practical advantages. Additionally, we incorporate a tunable back-off mechanism into our load-balancing scheme to reduce the classical communication load in the network. To study the policy, we consider a homogeneous star network topology that has the EGS at its center, and model it as a queueing system with requests that arrive according to a Poisson process and whose service times are exponentially distributed. We provide an asymptotic analysis of the system by deriving a set of differential equations that describe the dynamics of the mean-field limit and provide expressions for the corresponding unique equilibrium state. Consistent with analogous results from randomized load-balancing for classical systems, we observe a significant decrease in the average request processing time when the number of choices d increases from one to two during the sampling process, with diminishing returns for a higher number of choices. We also observe that our mean-field model provides a good approximation to study even moderately-sized systems.

Figures (7)

• Figure 1: Architecture of an EGS with $m$ resources -- here, BSAs ($S_j$). $N$ nodes ($D_i$) are connected to the EGS via classical and quantum channels.
• Figure 2: Average response time of an EGS deploying the $d$-choices policy, as a function of the number of choices $d$.
• Figure 3: Average response time of an EGS implementing $d$-choices policy as a function of back-off rate $\gamma$.
• Figure 4: Average response time as a function of server-to-queue ratio $r = \frac{m}{n}$, with varying $m$ and fixed $n = 200$.
• Figure 5: Average response time of $\mathop{\mathrm{JSQ}}\nolimits(d)$ and $\mathop{\mathrm{SLQ}}\nolimits(d)$ as a function of the number of choices $d$.

Theorems & Definitions (4)

• Remark 1
• Theorem 1
• Theorem 2
• proof