Quantum computing is becoming an increasingly popular topic in computer science. Some quantum computers are already in use but their operation is expensive. To explore quantum algorithms, quantum simulators are an important tool for benchmarking and sanity checks. On classical hardware, simulation of quantum states is hard due to their exponential nature. To address this problem, various techniques are used. In particular, tensor networks, a mathematical formalism, are advantageous for this task. General calculations then correspond to contraction problems in the network. In this thesis, Tree Tensor Networks are employed for the simulation process of quantum circuits. A framework for general operations on these tree tensors is provided, and a basic understanding of feasibility conveyed. This approach shows its effectiveness on well-structured problems. The entanglement structure in these problems allows efficient simulation, without explicit construction of the full state vector. Instead, the quantum state is encoded in a Tree Tensor Network and their special properties are used for simplified computation. Additionally, approximative techniques are possible, which imitate noise in current quantum hardware in comparison to perfect simulation. This lays a foundation for a wide range of applications in quantum computing.