In this thesis the matrix product state(MPS) formalism is applied to simulate a device created for remote detection in atomic spin chains. Although simulation of the full device quickly becomes infeasible for direct algorithms, MPS allowed for highly accurate simulations while requiring only modest computational resources. It has been verified that the simulation conserves energy and maintains normalization. Furthermore, the simulation is shown to successfully perform both a coherent real-time evolution and iteration towards the ground state. Thus MPS is a very promising tool that has potential to serve as a guide for further experiment as well as a tool to understand experimental results.