Quantum communication can enable new features that are provably impossible with classical communication alone. However, the optical fibers used to send the quantum information are inherently lossy. To overcome the exponential losses over distance so-called quantum repeaters are needed to amplify the signal. As opposed to memory-based approaches, the third generation of quantum repeaters, also called one-way quantum repeaters do not require two-way communication thus enabling very high communication rates. In particular, the one-way quantum repeater based on photonic tree states proposed
by Borregaard et al. (2019) realizes this task with a very modest amount of resources. Nevertheless, the method considered is susceptible to operational errors. In this work, we propose the use of code concatenation of a stabilizer code and the tree code, so that by measuring stabilizers of the stabilizer code and applying the syndrome corrections we can achieve a fault-tolerant one-way quantum repeater. In order to do so, we present a detailed protocol that uses the 5-qubit code. Moreover, we develop the first fully general simulation framework for studying the performance of tree-code based one-way quantum repeater
chains, which in this thesis is used to perform an analysis of the proposed
protocol. We find that the code-concatenation protocol under consideration has a similar tolerance against operational errors to the protocol proposed by Borregaard et al. (2019). Unfortunately, we are not able to draw a distinction between the tolerance of the two approaches. We do however suggest modified protocols that may provide fault tolerance. Studying these is beyond the scope of this thesis.

The quantum internet will allow for communication via qubits, enabling for improved clock synchronization, blind quantum computing and quantum key distribution. Key components of such a quantum network are quantum repeaters, which help to overcome the exponential loss of photons in optical fibers. In this thesis we focus on one type of quantum repeater based on atomic ensembles. In particular, we build a versatile and elaborate simulation model based on a discrete event simulator for quantum networks, capable of simulating quantum repeater chains of arbitrary length with a vast range of tunable simulation parameters. We validate this model by comparing it to an analytical one and investigate the effects of additional sources of noise that cannot be taken into account in the analytical model. Furthermore, we give a detailed theoretical overview and performance comparison of two types of quantum memories based on atomic ensembles: atomic frequency comb and electromagnetically induced transparency. Finally, we present two integer linear programming formulations for determining the optimal positioning of quantum repeaters in two spatial dimensions and demonstrate their use on a European-scale network.