Simulating the time evolution of quantum systems is an application of quantum computing of great importance to many fields such as chemistry, physics and optimization. Recent works Carrera2020 apply extrapolation techniques to product formulas with promising performance in practical problems. The analytical quantification of the error of such methods is a challenging problem. In this thesis, we develop a series expansion expression for the extrapolation error based on the Baker-Campbell-Hausdorff formula, together with a python algorithm to compute the error by truncating this series. The complexity of the algorithm is analyzed and practical aspects of the implementation are discussed. Finally, the approximation obtained from this algorithm is showcased on an example system.
This is the code developed as part of my Master's thesis at ETH Zurich & IBM Research under the supervision of Almudena Carrera Vazquez, Stefan Wörner and Prof. Ralph Hiptmair.
matrix_extrapolation - python module; contains a framework for Hamiltonian simulation using product formulas & extrapolation, based on numpy and mpmath, as well as the extrapolation error series expansion algorithm. Install it by running
pip install path/to/this/repo
scripts - scripts showcasing the usage of the module. Used to create the plots for my thesis report.