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We present a detailed description of the diagrammatic technique, recentlydevised in [V. V. Kuzmin et.al., npj Quantum Information 5, 115 (2019)], forsemi-analytical description of large-scale quantum-repeater networks. Thetechnique takes into account all essential experimental imperfections,including dissipative Liouville dynamics of the network quantum memories andthe classical communication delays. The results obtained with the semi-analyticmethod match the exact Monte Carlo simulations while the required computationalresources scale only linearly with the network size. The presented approachopens new possibilities for the development and efficient optimization offuture quantum networks.

Diagrammatic technique for simulation of large-scale quantum repeater networks with dissipating quantum memories