An on-demand resource allocation algorithm for a quantum network hub and its performance analysis

TL;DR

The paper addresses efficient on-demand resource allocation for quantum network hubs (EGS) by modeling entanglement-generation requests as Poisson sessions processed by an Erlang loss system. It introduces three practical service models that capture batching and calibration realities of near-term quantum hardware, derives stationary distributions and blocking probabilities, and proves an insensitivity theorem showing results depend only on mean durations of attempts and calibrations. Numerical evaluations using discrete-time and continuous-time simulations validate the analytic expressions under homogeneous and non-homogeneous traffic, confirming the robustness of the insensitivity property. The findings provide a concrete analytic framework and simulation toolkit for performance-driven resource provisioning in quantum networks, with potential to guide design and control of scalable EGS-based architectures.

Abstract

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 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 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 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.

Figures (18)

• Figure 1: A simple quantum network with end nodes $A$ and $C$ wishing to share entanglement, and an intermediate node $B$ assisting them with the task. Initially, two entangled links -- $\ket{\Psi^+}_{AB}$ between $A$ and $B$ and $\ket{\Psi^+}_{BC}$ between $B$ and $C$ -- are established. $B$ then performs a swapping operation to directly entangle $A$ and $C$'s qubits. Depending on the distance between $A$ and $C$, direct generation of entanglement (without an intermediate node), may not be feasible.
• Figure 2: Entanglement generation with a Bell state analyzer. Entangled photons travel towards the BSA, which carries out a probabilistic entanglement swap. At the BSA, photons pass through a beam splitter whose output ports are connected to a pair of detectors. The digital logic unit reads out measurement results and determines if a swap was successful. Results are classically communicated to nodes $A$ and $B$, whose qubits become entangled upon a successful event.
• Figure 3: End nodes being serviced by an EGS with a pool of three BSAs.
• Figure 4: Intermediate quantum network nodes leveraging the EGS to interconnect their respective quantum local area networks.
• Figure 5: Strict resource reservation service model. A session consists of multiple EPR pair generation attempts, denoted by A$_i$, $i=1,\dots,M$. A calibration period is carried out after every $m$ attempts. In the "multiple EPR pair generation" variant of this service model, an admitted session does not relinquish resources for its entire duration, while in the "single EPR pair generation" variant, the session ends after a successful attempt.

Theorems & Definitions (13)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5
• Definition 6
• Theorem 1
• Theorem 2
• Remark 1
• Remark 2