Fast and reliable entanglement distribution with quantum repeaters: Principles for improving protocols using reinforcement learning

Abstract

Future quantum technologies such as quantum communication, quantum sensing, and distributed quantum computation, will rely on networks of shared entanglement between spatially separated nodes. In this work, we provide improved protocols and policies for entanglement distribution along a linear chain of nodes, both homogeneous and inhomogeneous, that take practical limitations into account. For a wide range of parameters, our policies improve upon previously known policies, such as the “swap-as-soon-as-possible” policy, with respect to both the waiting time and the fidelity of the end-to-end entanglement. This improvement is greatest for the most practically relevant cases, namely, for short coherence times, high link losses, and highly asymmetric links. To obtain our results, we model entanglement distribution using a Markov decision process, and then we use the 𝑄-learning reinforcement-learning (RL) algorithm to discover alternative policies. These policies are characterized by dynamic, state-dependent memory cutoffs, and collaboration between the nodes. In particular, we quantify this collaboration between the nodes. Our quantifiers tell us how much “global” knowledge of the network every node has, specifically, how much knowledge two distant nodes have of each other’s states. In addition to the usual figures of merit, these quantifiers add an extra dimension to the performance analysis and practical implementation of quantum repeaters. Finally, our understanding of the performance of large quantum networks is currently limited by the computational inefficiency of simulating them using RL or other optimization methods. The other main contribution of our work is to address this limitation. We present a method for nesting policies in order to obtain policies for large repeater chains. By nesting our RL-based policies for small repeater chains, we obtain policies for large repeater chains that improve upon the swap-as-soon-as-possible policy, and thus we pave the way for a scalable method for obtaining policies for long-distance entanglement distribution under practical constraints.