Resource Placement for Rate and Fidelity Maximization in Quantum Networks

TL;DR

The paper tackles the challenge of planning quantum network infrastructure by formulating a resource placement problem that maximizes a joint rate-fidelity utility for multiple user pairs. It introduces two ILP-based formulations (path-based and link-based) that incorporate spatial multiplexing of quantum memories, memory coherence constraints, and repeater budgets, providing tractable linearizations and demonstrating scale invariance. Through evaluations on a synthetic dumbbell topology and real-world ESnet and SURFnet topologies, the work reveals how repeater spacing, memory capacities, and end-node coherence times shape optimal repeater deployment and end-to-end entanglement performance, and it highlights runtime planning implications under varying workload models. The results suggest that spatial multiplexing can achieve high end-to-end rates with modest coherence-time requirements, and they underscore the importance of planning assumptions for runtime performance. The framework and insights offer a practical path toward deploying scalable quantum networks within existing infrastructure.

Abstract

Existing classical optical network infrastructure cannot be immediately used for quantum network applications due to photon loss. The first step towards enabling quantum networks is the integration of quantum repeaters into optical networks. However, the expenses and intrinsic noise inherent in quantum hardware underscore the need for an efficient deployment strategy that optimizes the allocation of quantum repeaters and memories. In this paper, we present a comprehensive framework for network planning, aiming to efficiently distributing quantum repeaters across existing infrastructure, with the objective of maximizing quantum network utility within an entanglement distribution network. We apply our framework to several cases including a preliminary illustration of a dumbbell network topology and real-world cases of the SURFnet and ESnet. We explore the effect of quantum memory multiplexing within quantum repeaters, as well as the influence of memory coherence time on quantum network utility. We further examine the effects of different fairness assumptions on network planning, uncovering their impacts on real-time network performance.

Figures (10)

• Figure 1: An example of quantum network planning for a linear chain with $3$ potential locations for repeaters and a maximum of two memories per path. An instance of end-to-end entanglement generation is shown, where solid (dashed) lines represent successful (failed) attempts on links. The line connecting two memories inside a repeater indicates a successful Bell state measurement. The gray node $2$ shows that no repeater is placed at that location.
• Figure 2: (a) Dumbbell topology with $|Q|=n$ user pairs and 10 potential places for repeater placement (dashed circles), (b) optimal ebit rate per user pair, (c) optimal end-to-end fidelity, and (d) number of used repeaters as a function of the backbone link length.
• Figure 3: The effect of $q_s$ on the average end-to-end rate and average fidelity for $|Q|=6$ user pairs in our synthetic topology (figure \ref{['fig:dumbbell_topology']}.a)
• Figure 4: Optimal locations of repeaters for the augmented subgraph of the ESnet including nodes in the East Coast and the Midwest. The black circles (open and filled) denote the auxiliary nodes placed to make the longest link $100$km long. The optimization solution is shown as filled circles which indicate the locations of nodes turned into repeaters while open circles are not used. Some end nodes are shifted to improve readability.
• Figure 5: ESnet network planning on the ESnet augmented network graph where we place additional repeaters to upper bound the maximum link length $L_0$ (see main text for details). The legend also shows the number of potential repeater locations after the augmentation. Here, we set the memory capacity of repeaters and end users to be $W_E=D=10$.