论文标题

使用马尔可夫决策过程对近期量子网络协议的设计和分析

On the design and analysis of near-term quantum network protocols using Markov decision processes

论文作者

Khatri, Sumeet

论文摘要

量子互联网是量子信息科学研究的前沿之一。它将彻底改变我们交流和执行其他任务的方式,并且将允许使用当前的古典互联网进行不可能的任务。量子互联网的骨干是在全球分布的纠缠,以允许在长距离进行此类新型应用程序。目前正在实现实验进度以小规模实现量子网络,但是仍然需要进行大量理论工作,以了解如何最好地分发纠缠,尤其是在考虑到近期量子技术的局限性的情况下。这项工作为实现这一目标提供了第一步。在这项工作中,我们基于马尔可夫决策过程(MDPS)制定了近期量子网络的理论,我们表明MDP为对特定实现平台不可知的近期量子网络的模型协议提供了一个精确而系统的数学框架。我们首先简化了先前工作中引入的基本链接的MDP,并为基本链接的策略提供新的结果。特别是,我们表明众所周知的内存切割策略是最佳的。然后,我们展示了如何使用基本链接MDP分析量子网络协议,在该协议中,我们在创建端到端链接之前等待所有基本链接处于活动状态。然后,我们将MDP形式主义扩展到两个基本链接,这对于分析更复杂的量子网络协议很有用。在这里,作为新结果,我们得出了线性程序,这些程序为我们提供了有关端到端链接的预期保真度和等待时间的最佳稳态策略。

The quantum internet is one of the frontiers of quantum information science research. 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, especially with the limitations of near-term quantum technologies taken into account. This work provides an initial step towards this goal. In this work, we lay out a theory of near-term quantum networks based on Markov decision processes (MDPs), and we show that MDPs provide a precise and systematic mathematical framework to model protocols for near-term quantum networks that is agnostic to the specific implementation platform. We start by simplifying the MDP for elementary links introduced in prior work, and by providing new results on policies for elementary links. In particular, we show that the well-known memory-cutoff policy is optimal. Then we show how the elementary link MDP can be used to analyze a quantum network protocol in which we wait for all elementary links to be active before creating end-to-end links. We then provide an extension of the MDP formalism to two elementary links, which is useful for analyzing more sophisticated quantum network protocols. Here, as new results, we derive linear programs that give us optimal steady-state policies with respect to the expected fidelity and waiting time of the end-to-end link.

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