Diagrammatic Technique For Simulation Of Large-Scale Quantum Repeater Networks With Dissipating Quantum Memories

We present a detailed description of the diagrammatic technique for a semianalytical description of large-scale quantum repeater networks devised recently by V. V. Kuzmin et al. [npj Quantum Inf. 5, 115 (2019)]. The technique takes into account all essential experimental imperfections, including continuous dissipative Liouville dynamics of the network quantum memories and the classical communication delays. The results obtained with the semianalytic method match the exact Monte Carlo simulations while the required computational resources scale only linearly with the network size, thus allowing for precise comparison and optimization of large-scale quantum networks subjected to relevant realistic imperfections. We illustrate the potential of the method by optimizing the secret key rate in one- and two-dimensional quantum networks for a range of network sizes and memory coherence times. The presented approach opens new possibilities for the development and efficient optimization of future quantum networks.