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

Abstract

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.

v2: 19+37 pages, 17 figures; updated references; minor changes to the structure and presentation; similar to the published version

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Cited by in corpus (8)

• Optimal entanglement distribution policies in homogeneous repeater chains with cutoffs
• Fast and reliable entanglement distribution with quantum repeaters: principles for improving protocols using reinforcement learning
• Entanglement Distribution in the Quantum Internet: Knowing when to Stop!
• ReQuSim: Faithfully simulating near-term quantum repeaters
• Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies
• Constant Overhead Entanglement Distillation via Scrambling
• A resource- and computationally-efficient protocol for multipartite entanglement distribution in Bell-pair networks
• Optimising entanglement distribution policies under classical communication constraints assisted by reinforcement learning