The goal of quantum application scheduling is to enable the execution of applications on a quantum network. As the final step in the application scheduling process, program scheduling locally schedules execution of blocks of instructions on each node by defining so-called node schedules. In this thesis, we present a formal definition of program scheduling and propose success metrics to evaluate the quality of node schedules. We implement program scheduling using the framework of Resource-Constrained Project Scheduling Problem (RCPSP) and and simulate the execution of node schedules. By evaluating the performance of program scheduling on datasets with diverse quantum applications including quantum key distribution and blind quantum computing, we observe that heuristic-driven approaches achieve comparable results to optimal program scheduling while requiring fewer computational resources. Our work offers valuable insights into the translation of classical scheduling problems into the quantum domain, contributing to the advancement of quantum application scheduling.

There has been a lot of research focused on the next generation of the internet, the so-called quantum networks. This analysis has been so far limited to mostly symmetrical architectures, but any near-term realisations of quantum networks using existing fibre topologies will contain asymmetry. In this thesis, we investigate how midpoint asymmetry affects quantum repeater protocols implemented with atomic ensembles. We extend the existing simulation framework to allow for midpoint asymmetry. By simulating asymmetry in elementary links, we show that the performance of an elementary link executing quantum key distribution decreases with an increasing degree of asymmetry. This effect can be mitigated by individual optimisation of photon sources at both ends of the elementary link. We present a way how to reduce the search space of such optimisations by developing a heuristic. The contributions of this thesis provide a crucial starting point for investigations of asymmetry in quantum repeater chains.