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arXiv:2306.09216

Scalable Quantum Networks: Congestion-Free Hierarchical Entanglement Routing with Error Correction

Hyeongrak Choi, Davis, Marc G., Álvaro G. Iñesta, Dirk Englund

Published Jun 15, 2023• 3 citations
arXivHTMLPDF

Abstract

We introduce Quantum Tree Networks (QTN), an architecture for hierarchical multi-flow entanglement routing. The network design is a $k$-ary tree where end nodes are situated on the leaves and routers at the internal nodes, with each node connected to $k$ nodes in the child layer. The channel length between nodes grows with a rate $a_k$, increasing as one ascends from the leaf to the root node. This construction allows for congestion-free and error-corrected operation with qubit-per-node overhead to scale sublinearly with the number of end nodes, $N$. The overhead for a $k$-ary QTN scales as $\mathcal{O}(N^{\log_k a_k} \cdot \log_k N)$ and is sublinear for all $k$ with minimal surface-covering end nodes. More specifically, the overhead of quarternary ($k=4$) QTN is $\sim \mathcal{O}(N^{0.25}\cdot\log_4 N)$. Alternatively, when end nodes are distributed over a square lattice, the quaternary tree routing gives the overhead $\sim \mathcal{O}(\sqrt{N}\cdot\log_4 N)$. Our network-level simulations demonstrate a size-independent threshold behavior of QTNs. Moreover, tree network routing avoids the necessity for intricate multi-path finding algorithms, streamlining the network operation. With these properties, the QTN architecture satisfies crucial requirements for scalable quantum networks.

DOI
10.48550/arxiv.2306.09216

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We introduce Quantum Tree Networks (QTN), an architecture for hierarchical multi-flow entanglement routing. The network design is a kkk-ary tree where end nodes are situated on the leaves and routers at the internal nodes, with each node connected to kkk nodes in the child layer. The channel length between nodes grows with a rate aka_kak​, increasing as one ascends from the leaf to the root node. This construction allows for congestion-free and error-corrected operation with qubit-per-node overhead to scale sublinearly with the number of end nodes, NNN. The overhead for a kkk-ary QTN scales as O(Nlog⁡kak⋅log⁡kN)\mathcal{O}(N^{\log_k a_k} \cdot \log_k N)O(Nlogk​ak​⋅logk​N) and is sublinear for all kkk with minimal surface-covering end nodes. More specifically, the overhead of quarternary (k=4k=4k=4) QTN is ∼O(N0.25⋅log⁡4N)\sim \mathcal{O}(N^{0.25}\cdot\log_4 N)∼O(N0.25⋅log4​N). Alternatively, when end nodes are distributed over a square lattice, the quaternary tree routing gives the overhead ∼O(N⋅log⁡4N)\sim \mathcal{O}(\sqrt{N}\cdot\log_4 N)∼O(N​⋅log4​N). Our network-level simulations demonstrate a size-independent threshold behavior of QTNs. Moreover, tree network routing avoids the necessity for intricate multi-path finding algorithms, streamlining the network operation. With these properties, the QTN architecture satisfies crucial requirements for scalable quantum networks.
We propose quantum tree network (QTN) designs that are 1) free from congestion in multiflow communications, 2) optimal routing with only local information (self-information) and 3) completely covers 2D surface, 4) with only logarithmic overhead. If the channel is dominated by the insertion loss and the communication is limited by the local gates, as in current state-of-the-art technologies, the overhead is log(N), while this is relaxed to the general cases with poly-log overhead by engaging repeater chains in the long range communication.
In entanglement distribution networks, communication between two nodes necessitates the generation of end-to-end entanglement by entanglement swapping at intermediate nodes. Efficiently creating end-to-end entanglements over long distances is a key objective. In our prior study on asynchronous routing, we enhanced these entanglement rates by leveraging solely the local knowledge of the node's entanglement links. This was achieved by creating a tree structure, particularly a destination-oriented directed acyclic graph (DODAG) or a spanning tree, eliminating synchronous operations and conserving unused entanglement links. In this article, we present a multi-tree approach with multiple DODAGs designed to improve end-to-end entanglement rates in large-scale networks, specifically catering to a range of network topologies, including grids and barbells, as well as realistic topologies found in research testbeds like ESnet and Internet2. Our simulations show a marked improvement in end-to-end entanglement rates for specific topologies compared to the single-tree method. This study underscores the promise of asynchronous routing schemes in quantum networks, highlighting the effectiveness of asynchronous routing across different network topologies and proposing a superior routing tactic.
The quantum network is designed to connect numerous quantum nodes and support various ground-breaking quantum applications. Most of these applications require communicating parties to share entangled pairs. Therefore, entanglement routing, a technology distributing entangled pairs between distant quantum nodes, plays a vital role in realizing quantum networks’ capability. However, due to the limitation of quantum memory size and quantum decoherence, the entangled pairs shared by adjacent quantum nodes can hardly satisfy concurrent entanglement routing requests, thus leading to severe network congestion. In this paper, we propose a novel congestion mitigation (CM) scheme to tackle such bottleneck problems. The basic idea of CM is to “recycle” idle link-level entanglement resources from well-resourced links to bottleneck links utilizing a unique enabling technology of quantum networks, called entanglement swapping. CM can increase the capacity of each bottleneck link, thus overcoming resource limitations to improve resource utilization and network throughput. To complete our work, we also propose a swapping-based entanglement routing design, including path selection and resource allocation algorithms. Extensive simulations show that our design can significantly alleviate network congestion and improve the request service rate of quantum networks compared to the traditional entanglement routing designs.
How to efficiently distribute entanglement over large-scale quantum networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks where each link is characterized by a trade-off between the entanglement generation rate and fidelity. For such networks, we look at the two following problems: the one of finding the best path to connect any two given nodes, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. Two entanglement distribution models are considered: one where entangled qubits are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. The paper proposes of a quite general methodology that uses continuous fidelity curves (i.e., entanglement generation fidelity vs. rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the link models and networks considered, it is proven that the algorithm always converges to the optimal solution. It is also shown through simulation that the execution time grows polynomially with the number of network nodes (growing with a power between 111 and 1.41.41.4, depending on the network)
The quantum network that allows users to communicate in a quantum way will be available in the foreseeable future. The network capable of distributing Bell state entangled pairs faces many challenges due to entanglement decoherence and limited network performance, especially when the network scale is enormous. Many entanglement distribution protocols have been proposed so far, and most of them are in a centralized and synchronized manner, which may be infeasible in large-scale networks. As such, in this paper, we propose a full spontaneous version of quantum networks in which the quantum nodes autonomously manage multiple entanglement distribution requests. However, one major issue is that quantum nodes have little knowledge about the network, especially the congestion (e.g., some nodes may have no usable quantum memories). We present a routing algorithm to adaptive evaluate the congestion on the neighbor nodes to avoid potential congestion. We use SimQN, the new network layer simulation platform built by our research team, to evaluate our proposed design. The result demonstrates that it can adapt to changes in network resources and reduce the drop rate that eventually leads to a higher entanglement distribution rate but remains fair for multiple requests to use the network resources fairly and achieve a more balanced throughput.