Bachelor Thesis Laurin Demmler Introduction

This bachelor thesis explores three concepts in the space of MPS/MPO/TEBD. Firstly, a benchmark of a variational truncation method is introduced. Later, the TEBD algorithm is benchmarked and the result from a paper (by Zhou, Yiqing and Stoudenmire, E. Miles and Waintal, Xavier, doi: 10.1103/PhysRevX.10.041038) is reproduced. The last part of this thesis aims to compare the error propagation of the time evolved equal time correlator in the Schrödinger and Heisenberg picture. One can choose between:

• variational truncation vs. MPS_exact
• variational truncation vs. MPS_step
• TEBD benchmark
• two qubit gate fidelity (reproduction of the paper)
• lightcone like structure of the correlator
• absolute and relative error propagation in the lightcone structure
• performance comparison in the Schrödinger/Heisenberg picture

How to use

In order to use the simulations, please create a file called config.json in the same directory as main.py. It should have the following format:

{
   "SimulationType": "MPS_exact/MPS_step/TEBD/Two Qubit Mean Fidelity TEBD/Lightcone/Relative Error/Absolute Fixed Error/Absolute Sum Error Average/Performance" (as str),
   "Qubits": Number of Qubits (as int),
   "MaxDepth": Maximal simulation depth (as int),
   "chiMax": Maximal bond dimension in Schrödinger picture (as int),
   "chiOperator": Maximal bond dimension in Heisenberg picture (as int),
   "offset": For MPS_exact and MPS_step if more than one SystemSize is simulated/ 0 for all other applications (as int),
   "LightconeType": "TEBD/Operator" (Schrödinger/Heisenberg as str),
   "TimeStepType": "Full/Half" (full or half timesteps as str)
}

Please run the simulation by executing main.py from Simulation_TEBD_MPS.

Acknowledgements

Thanks to Prof. Frank Pollmann, M.Sc. Sheng-Hsuan Lin, Xaver Kainz and Joshua Jeschek