Tree Tensor Networks (TTNs) offer a scalable and organized framework for expressing high-dimensional quantum states and simulating quantum circuits. The application of TTNs is addressed in this thesis, with an emphasis on creating parallelization techniques to improve computing effectiveness. By making use of the hierarchical structure of TTNs, these approaches seek to divide tensor operations—like contractions and orthonormalizations—across different processing units for concurrent execution.

Nevertheless, there were a number of difficulties in putting these parallelization techniques into practice. Efficient execution was hampered by problems including inconsistent structural representation of intermediate nodes and mismatched tensor dimensions during contraction. To ensure compatibility across operations, these difficulties necessitated iterative improvements to the tensor representations, such as modifying the contraction dimensions and dynamically restructuring the tensors.

In spite of these challenges, our work shows the potential of parallelized TTNs in simulations of quantum circuits and offers a strong basis for future studies. The results and insights gained highlight both the opportunities offered by these applications as well as the complexities of scaling TTNs for high-performance quantum simulations, hence contributing to the advancement of tensor network algorithms in quantum computing.