Finding Exponential Product Formulas of Higher Orders
Abstract
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves important symmetries of the system dynamics. We focuse on two algorithms of constructing higher-order exponential product formulas. The first is the fractal decomposition, where we construct higher-order formulas recursively. The second is to make use of the quantum analysis, where we compute higher-order correction terms directly. As interludes, we also have described the decomposition of symplectic integrators, the approximation of time-ordered exponentials, and the perturbational composition.
Cite
@article{arxiv.math-ph/0506007,
title = {Finding Exponential Product Formulas of Higher Orders},
author = {Naomichi Hatano and Masuo Suzuki},
journal= {arXiv preprint arXiv:math-ph/0506007},
year = {2011}
}
Comments
22 pages, 9 figures. To be published in the conference proceedings ''Quantum Annealing and Other Optimization Methods," eds. B.K.Chakrabarti and A.Das (Springer, Heidelberg)