Utilizing the recent generalization of the Time Dependent Variational Principle (TDVP) for Tree Tensor Networks (TTN) by [1], this thesis provides a TDVP implementation that is discussed along with TTN fundamentals extensively and then used to simulate quantum circuit operations for circuits that interact with an environment (or itself). TTNs allow for well-performing computation of operations on the Hilbert space of a multi-qubit system. The TDVP algorithm for TTNs can be used to time-evolve a quantum state under the action of a system Hamiltonian, which is derived for a model of five qubits, where each qubit is connected to a single boson. The system dynamics are constituted of three parts: Nearest-neighbor qubit-qubit interaction, nearest-neighbor qubit-boson interaction and application of quantum circuit gates. The goal is to apply this methodology to the 5-qubit quantum error correction (QEC) code by [2] and observe the impact a bosonic bath and qubit-qubit interaction have on the fidelity of the error correction. The model and error correction setup is similar to [3], where for the same QEC code a similar reduction of circuit fidelity is observed as in this thesis. The presented algorithms and model are versatile and reliable. However, challenges arise when applying the algorithm to the presented model as the performance demand for accurate simulation is the main limitation to the number of presented configurations. A discussion of possible improvements to the implementations of the algorithms as well as to the model covers several aspects that could be included in future work.     «

Utilizing the recent generalization of the Time Dependent Variational Principle (TDVP) for Tree Tensor Networks (TTN) by [1], this thesis provides a TDVP implementation that is discussed along with TTN fundamentals extensively and then used to simulate quantum circuit operations for circuits that interact with an environment (or itself). TTNs allow for well-performing computation of operations on the Hilbert space of a multi-qubit system. The TDVP algorithm for TTNs can be used to time-evolve a...     »