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arXiv:2304.08921

Networking quantum networks with minimum cost aggregation

Koji Azuma

Published Apr 18, 2023• 0 citations
arXivHTMLPDF

Abstract

A quantum internet holds promise for achieving distributed quantum sensing and large-scale quantum computer networks, as well as quantum communication among arbitrary clients all over the globe. The main building block is efficient distribution of entanglement, entangled bits (ebits), between clients with fixed error, irrespective of their distance. In practice, this should be accomplished across multiple quantum networks, analogously to what the current Internet does in conventional communication. However, existing quantum repeater schemes for efficient distribution of ebits over long distances work only on linear networks. Besides, there was no prescription on how to choose such linear networks from quantum networks with arbitrary topology. Here we present a practical recipe on how to aggregate quantum networks with arbitrary topology in order to give clients ebits with fixed error efficiently, regardless of their distance. This recipe is based on combination of two new concepts of minimum cost aggregation and network concatenation. Our recipe forms the basis of designing a quantum internet protocol for networking self-organizing quantum networks to make a global-scale quantum internet.

DOI
10.48550/arxiv.2304.08921

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A quantum internet holds promise for achieving distributed quantum sensing and large-scale quantum computer networks, as well as quantum communication among arbitrary clients all over the globe. The main building block is efficient distribution of entanglement, entangled bits (ebits), between clients with fixed error, irrespective of their distance. In practice, this should be accomplished across multiple quantum networks, analogously to what the current Internet does in conventional communication. However, existing quantum repeater schemes for efficient distribution of ebits over long distances work only on linear networks. Besides, there was no prescription on how to choose such linear networks from quantum networks with arbitrary topology. Here we present a practical recipe on how to aggregate quantum networks with arbitrary topology in order to give clients ebits with fixed error efficiently, regardless of their distance. This recipe is based on combination of two new concepts of minimum cost aggregation and network concatenation. Our recipe forms the basis of designing a quantum internet protocol for networking self-organizing quantum networks to make a global-scale quantum internet.
Abstract A quantum version of an internet, called a quantum internet, holds promise for achieving distributed quantum sensing and large-scale quantum computer networks, as well as quantum communication among arbitrary clients all over the globe. The main building block is efficient distribution of entanglement—entangled bits (ebits)—between arbitrary clients in a quantum network with error bounded by a constant, irrespective of their distance. In practice, this should be accomplished across multiple self-organising quantum networks, analogously to what the current internet does in conventional communication. Here we present a practical recipe on how to efficiently give arbitrary clients ebits with error bounded by a constant, regardless of their distance, across multiple quantum networks. This recipe is composed of two new concepts, minimum cost aggregation and network concatenation. Our recipe forms the necessary basis of designing a quantum internet protocol for networking self-organising quantum networks to make a global-scale quantum internet.
The quantum internet holds promise for accomplishing quantum teleportation and unconditionally secure communication freely between arbitrary clients all over the globe, as well as the simulation of quantum many-body systems. For such a quantum internet protocol, a general fundamental upper bound on the obtainable entanglement or secret key has been derived [K. Azuma, A. Mizutani, and H.-K. Lo, Nat. Commun. 7, 13523 (2016)]. Here we consider its converse problem. In particular, we present a universal protocol constructible from any given quantum network, which is based on running quantum repeater schemes in parallel over the network. For arbitrary lossy optical channel networks, our protocol has no scaling gap with the upper bound, even based on existing quantum repeater schemes. In an asymptotic limit, our protocol works as an optimal entanglement or secret-key distribution over any quantum network composed of practical channels such as erasure channels, dephasing channels, bosonic quantum amplifier channels, and lossy optical channels.
Quantum networks play a pivotal role in quantum information science, which not only provide a secure communication platform for remote access to quantum computers but also serve as the strategic core for achieving large-scale quantum information processing, forming the foundational infrastructure for the future global-scale quantum internet. Quantum teleportation, which enables the transmission of unknown quantum states over long distances by employing quantum entanglement together with classical communication, is essential for the distribution of quantum resources in the construction of the global-scale quantum internet. To realize a global-scale quantum internet, quantum repeater protocols represent one of the most promising approaches for enabling quantum communication between any nodes. This concise review presents representative experimental demonstrations of quantum teleportation for constructing quantum networks across different physical platforms. Along this trajectory, the review discusses current challenges, open issues, and future perspectives toward scalable and practical quantum internet.
The quantum internet is one of the frontiers of quantum information science. It will revolutionize the way we communicate and do other tasks, and it will allow for tasks that are not possible using the current, classical internet. The backbone of a quantum internet is entanglement distributed globally in order to allow for such novel applications to be performed over long distances. Experimental progress is currently being made to realize quantum networks on a small scale, but much theoretical work is still needed in order to understand how best to distribute entanglement and to guide the realization of large-scale quantum networks, and eventually the quantum internet, especially with the limitations of near-term quantum technologies. This work provides an initial step towards this goal. The main contribution of this thesis is a mathematical framework for entanglement distribution protocols in a quantum network, which allows for discovering optimal protocols using reinforcement learning. We start with a general development of quantum decision processes, which is the theoretical backdrop of reinforcement learning. Then, we define the general task of entanglement distribution in a quantum network, and we present ground- and satellite-based quantum network architectures that incorporate practical aspects of entanglement distribution. We combine the theory of decision processes and the practical quantum network architectures into an overall entanglement distribution protocol. We also define practical figures of merit to evaluate entanglement distribution protocols, which help to guide experimental implementations.
The development of a future global quantum communication network (or quantum Internet) will enable high-rate private communication and entanglement distribution over very long distances.However, the large-scale performance of ground-based quantum networks (which employ photons as information carriers through optical fibers) is fundamentally limited by fiber quality and link length, with the latter being a primary design factor for practical network architectures.While these fundamental limits are well established for arbitrary network topologies, the question of how to best design global architectures remains open.In this work, we introduce a large-scale quantum network model called weakly regular architectures.Such networks are capable of idealizing network connectivity, provide freedom to capture a broad class of spatial topologies, and remain analytically treatable.This allows us to investigate the effectiveness of large-scale networks with consistent connective properties and unveil critical conditions under which end-to-end rates remain optimal.Furthermore, through a strict performance comparison of ideal groundbased quantum networks with that of realistic satellite quantum communication protocols, we establish conditions for which satellites can be used to outperform fiber-based quantum infrastructure, rigorously proving the efficacy of satellite-based technologies for global quantum communications.
Imagine a Quantum Internet where people can freely establish physically secure communication channels or migrate quantum programs between anywhere in the world. What would it look like? Despite the very exciting recent advances around building prototypes of quantum networks, little is known about how lab-scale prototypes can be expanded into a global infrastructure that is as capacitated, robust, and cost-efficient as the digital Internet right now. Part of the difficulty lies in our lack of understanding of how the structure of a quantum network affects its capacity and performance when serving multi-commodity quantum communication demands. This article studies the problem of designing high-performance network topologies for the quantum Internet. Utilizing abstract models of the basic quantum network operations and an optimal entanglement distribution protocol, we characterize the capacity and performance of various candidate topologies for the quantum Internet, in terms of the rate of entanglement distribution between source-destination pairs and the fidelity of entangled pairs, respectively. We discuss the implications of our preliminary results, and propose directions for further investigation. As the feasibility of largescale quantum network deployment continues to increase, we hope this article can draw attention to these macroscopic design problems, such as topology design, which potentially have a profound influence on how the entire technology evolves, just as we have observed with the digital Internet in the past decades.