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IEEE International Conference on Sensing, Communication, and Networking (SECON)

Topology Design with Resource Allocation and Entanglement Distribution for Quantum Networks

Jiyao Liu, Xuanzhang Liu, Xinliang Wei, Yu Wang

Published Dec 2, 2024• 7 citations
Publisher

Abstract

Topology is one of the most critical properties of networks. Quantum networks, as a new type of network, have fundamentally different principles for establishing connections compared to classical networks, leading to distinct challenges in topology design. Finding the optimal topology for quantum networks to meet traffic demands is a crucial yet not fully understood problem. In this paper, we explore the topology design problem for quantum networks, considering both resource allocation and entanglement distribution. We propose and investigate both flow-based and path-based formulations, along with their associated solutions, aimed at minimizing the topology cost. For the path-based formulation, we also provide the first theoretical analysis of the cost associated with swapping strategies over a quantum path. Extensive simulations demonstrate that our enhanced path-based formulation is both efficient and effective.

DOI
10.1109/secon64284.2024.10934901

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Topology is one of the most critical properties of networks. Quantum networks, as a new type of network, have fundamentally different principles for establishing connections compared to classical networks, leading to distinct challenges in topology design. Finding the optimal topology for quantum networks to meet traffic demands is a crucial yet not fully understood problem. In this paper, we explore the topology design problem for quantum networks, considering both resource allocation and entanglement distribution. We propose and investigate both flow-based and path-based formulations, along with their associated solutions, aimed at minimizing the topology cost. For the path-based formulation, we also provide the first theoretical analysis of the cost associated with swapping strategies over a quantum path. Extensive simulations demonstrate that our enhanced path-based formulation is both efficient and effective.
Quantum networks are designed to transmit quantum bits (qubits) among quantum devices to enable new network resources for the applications. Entanglement distribution and entanglement swapping are fundamental procedures that are required in several network operations. However, they are probabilistic operations, which can lead to severe network performance degradation. This article investigates the engineering problem of resource allocation in quantum networks, considering factors like entanglement distribution probability, quantum memory characteristics, and fidelity. We model this as an optimization model to obtain an optimal solution. In particular, we formulate an integer linear programming (ILP) and develop a heuristic algorithm, aiming to minimize the number of required entangled qubit pairs (Bell pairs or EPR pairs) in any adjacent pair in the quantum network. Extensive simulations are performed to compare the performance of proposed ILP and heuristic. In all the cases, the heuristic produces a comparable solution to the optimal one. Simulation results ensure that the value of maximum utilized Bell pairs in a quantum network highly depends on the value of the probability of entangled pairs established, considering the time in the quantum memory besides the number of incoming requests.
This paper presents a novel algorithm for resource allocation within quantum networks leveraging topological structures. The core claim is to design an efficient resource allocation strategy that maximizes quantum computation effectiveness and resource utilization. The proposed mechanism dynamically allocates quantum computational resources based on the network's topology, optimizing the computational workflow. This addresses a critical challenge in quantum computing – efficient resource management – by introducing a new approach. The algorithm's effectiveness is demonstrated through theoretical analysis and a focus on key performance indicators such as qubit fidelity, computational latency, and overall resource throughput. The algorithm aims to improve the practicality and scalability of quantum computation within distributed quantum networks. The primary goal is to mitigate the limitations of traditional resource allocation methods, which often struggle to account for the complex and dynamic nature of quantum network topologies. This work contributes to the advancement of quantum networking and its potential for realizing robust and scalable quantum computation.
Distributed Quantum Computing (DQC) enables the execution of quantum circuits across multiple interconnected quantum processing units (QPUs), but requiring efficient qubit allocation and network topology design to optimize computational performance. Proper qubit allocation minimizes entanglement costs across QPUs, balances computational workload, and ensures efficient execution of quantum computing tasks. Meanwhile, network topology plays a crucial role in reducing entanglement routing complexity and communication overhead for remote quantum gate operations. In this paper, we propose a joint optimization framework for network topology design and qubit allocation in DQC to minimize the communication overhead. We formulate the problem as a tractable integer nonlinear programming model that explicitly incorporates entanglement routing, thereby ensuring a more tractable optimization process. To further improve computational efficiency, we present a partially linearized version of the problem, making it solvable using any classical optimization solver. Extensive simulations on both random and real-world quantum circuits validate the effectiveness of our proposed approach, demonstrating its capability to handle complex quantum circuits while reducing communication costs in DQC.
Distributing quantum entanglements over long distances is essential for the realization of a global scale quantum Internet. Most of the prior work and proposals assume an on-demand distribution of entanglements which may result in significant network resource under-utilization. In this work, we introduce Quantum Overlay Networks (QONs) for efficient entanglement distribution in quantum networks. When the demand to create end-to-end user entanglements is low, QONs can generate and store maximally entangled Bell pairs (EPR pairs) at specific overlay storage nodes of the network. Later, during peak demands, requests can be served by performing entanglement swaps either over a direct path from the network or over a path using the storage nodes. We solve the link entanglement and storage resource allocation problem in such a QON using a centralized optimization framework. We evaluate the performance of our proposed QON architecture over a wide number of network topologies under various settings using extensive simulation experiments. Our results demonstrate that QONs fare well by a factor of 40% with respect to meeting surge and changing demands compared to traditional non-overlay proposals. QONs also show significant improvement in terms of average entanglement request service delay over non-overlay approaches.
Quantum networking has been attracting growing attention in both academia and industry during recent years. Although many routing protocols have been proposed to optimize the network layer of quantum networks, another key networklayer problem is under-explored: the topology design problem. Existing work is limited to using structure topologies such as a ring or grid, using randomly generated topologies, or using existing Internet backbone infrastructure. Whether these choices are desired for quantum networks is not fully explained. We propose the quantum network topology design problem, for which a set of end users are given and we need to compute a set of repeaters and their locations and connectivities while ensuring the network performance, such as throughput, is optimized under the same infrastructure cost (e.g., number of repeaters). We present the methodology of designing topologies based on the unique characteristics of entanglement distribution networks and propose an algorithm called TriPlace to compute a topology for a given set of end users in different locations of a geographic region. The simulation results show that TriPlace incurs a lower infrastructure cost than all existing solutions while achieving similar throughput performance as the best of these solutions. We believe this work will start a new research problem for quantum networks and attract more future work.
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation, and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between quantum computers, it is imperative and crucial to exploit game theory for addressing challenges such as entanglement distribution and access, routing, topology extraction, and inference. Quantum networks provide the promising opportunity of employing quantum games owing to their inherent capability of generating and sharing quantum states. In addition, quantum games offer enhanced payoffs and winning probabilities, new strategies, and equilibria, which are unimaginable in classical games. Employing quantum game theory to solve fundamental challenges in quantum networks opens a new fundamental research direction necessitating inter-disciplinary efforts. In this article, we introduce a novel game-the-oretical framework for exploiting quantum strategies to solve – as an archetypal example – one of the key functionalities of a quantum network, namely, entanglement distribution. We compare quantum strategies with classical ones by showing the quantum advantages in terms of link fidelity improvement and latency decrease in communication. In the future, we will generalize our game framework to optimize entanglement distribution and access over any quantum network topology. We will also explore how quantum games can be leveraged to address other challenges like routing, optimization of quantum operations, and topology design.