Optimization of quantum-repeater networks using stochastic automatic differentiation

Quantum repeaters are envisioned to enable long-distance entanglement distribution. Analysis of quantum-repeater networks could hasten their realization by informing design decisions and research priorities. Determining derivatives of network properties is crucial toward that end, facilitating optimizations and revealing parameter sensitivity. Doing so, however, is difficult because the networks are discretely random. Here we use a recently developed technique, stochastic automatic differentiation, to automatically extract derivatives from discrete Monte Carlo simulations of repeater networks. With these derivatives, we optimize rate-fidelity tradeoffs in a repeater chain, determine the chain's sensitivity with respect to the coherence times of different nodes, and finally choose the locations of quantum repeaters in a two-dimensional plane to optimize the guaranteed quality of service between four end nodes. In particular, the technique enabled us to discover how the best achievable quality of service, the minimal number of repeaters required to improve a network, and the number of repeaters required to saturate the network scale with the physical size of the network.