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arXiv:2503.22292 · International Conference on Quantum Communications, Networking, and Computing (QCNC)

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

Guo Xian Yau, Thirupathaiah Vasantam, Gayane Vardoyan

Published Mar 31, 2025• 1 citation
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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.

DOI
10.1109/qcnc64685.2025.00011

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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.
To effectively support the execution of quantum network applications for multiple sets of user-controlled quantum nodes, a quantum network must efficiently allocate shared resources. We study traffic models for a type of quantum network hub called an Entanglement Generation Switch (EGS), a device that allocates resources to enable entanglement generation between nodes in response to user-generated demand. We propose an on-demand resource allocation algorithm, where a demand is either blocked if no resources are available or else results in immediate resource allocation. We model the EGS as an Erlang loss system, with demands corresponding to sessions whose arrival is modeled as a Poisson process. To reflect the operation of a practical quantum switch, our model captures scenarios where a resource is allocated for batches of entanglement generation attempts, possibly interleaved with calibration periods for the quantum network nodes. Calibration periods are necessary to correct against drifts or jumps in the physical parameters of a quantum node that occur on a timescale that is long compared to the duration of an attempt. We then derive a formula for the demand blocking probability under three different traffic scenarios using analytical methods from applied probability and queueing theory. We prove an insensitivity theorem which guarantees that the probability a demand is blocked only depends upon the mean duration of each entanglement generation attempt and calibration period, and is not sensitive to the underlying distributions of attempt and calibration period duration. We provide numerical results to support our analysis. Our numerical results suggest that there exist parameter regimes where it is beneficial for nodes to relinquish control of EGS resources during their calibration periods. This benefit is quantified by the blocking probability and the total entanglement generated in a fixed period of time. Our work is the first analysis of traffic characteristics at an EGS system and provides a valuable analytic tool for devising performance driven resource allocation algorithms.
To support the execution of multiple simultaneously-running quantum network applications, a quantum network must efficiently allocate shared resources. We study traffic models for a type of quantum network hub called an Entanglement Generation Switch (EGS), a device that allocates resources to enable entanglement generation between nodes in response to user-generated demand. We propose an on-demand resource allocation algorithm, where a demand is either blocked if no resources are available or else results in immediate resource allocation. We model the EGS as an Erlang loss system, with demands corresponding to sessions whose arrival is modelled as a Poisson process. To reflect the operation of a practical quantum switch, our model captures scenarios where a resource is allocated for batches of entanglement generation attempts, possibly interleaved with calibration periods for the quantum network nodes. Calibration periods are necessary to correct against drifts or jumps in the physical parameters of a quantum node. We then derive a formula for the demand blocking probability under three different traffic scenarios using analytical methods from applied probability and queueing theory. We prove an insensitivity theorem which guarantees that the probability a demand is blocked only depends upon the mean duration of each entanglement generation attempt and calibration period, and is not sensitive to their underlying distributions. Our numerical results support our analysis. Our work is the first analysis of traffic characteristics at an EGS system and provides a valuable analytic tool for devising performance driven resource allocation algorithms.
We study a quantum network that distributes entangled quantum states to multiple sets of users that are connected to the network. Each user is connected to a switch of the network via a link. All the links of the network generate bipartite Bell-state entangled states in each time-slot with certain probabilities, and each end node stores one qubit of the entanglement generated by the link. To create shared entanglements for a set of users, measurement operations are performed on qubits of link-level entanglements on a set of related links, and these operations are probabilistic in nature and are successful with certain probabilities. Requests arrive to the system seeking shared entanglements for different sets of users. Each request is for the creation of shared entanglements for a fixed set of users using link-level entanglements on a fixed set of links. Requests are processed according to First-Come-First-Served service discipline and unserved requests are stored in buffers. Once a request is selected for service, measurement operations are performed on qubits of link-level entanglements on related links to create a shared entanglement. For given set of request arrival rates and link-level entanglement generation rates, we obtain necessary conditions for the stability of queues of requests. In each time-slot, the scheduler has to schedule entanglement swapping operations for different sets of users to stabilize the network. Next, we propose a Max-Weight scheduling policy and show that this policy stabilizes the network for all feasible arrival rates. We also provide numerical results to support our analysis. The analysis of a single quantum switch that creates multipartite entanglements for different sets of users is a special case of our work.
Entanglement between quantum network nodes is often produced using intermediary devices - such as heralding stations - as a resource. When scaling quantum networks to many nodes, requiring a dedicated intermediary device for every pair of nodes introduces high costs. Here, we propose a cost-effective architecture to connect many quantum network nodes via a central quantum network hub called an Entanglement Generation Switch (EGS). The EGS allows multiple quantum nodes to be connected at a fixed resource cost, by sharing the resources needed to make entanglement. We propose an algorithm called the Rate Control Protocol (RCP) which moderates the level of competition for access to the hub's resources between sets of users. We proceed to prove a convergence theorem for rates yielded by the algorithm. To derive the algorithm we work in the framework of Network Utility Maximization (NUM) and make use of the theory of Lagrange multipliers and Lagrangian duality. Our EGS architecture lays the groundwork for developing control architectures compatible with other types of quantum network hubs as well as system models of greater complexity.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.