Finding Exponential Product Formulas of Higher Orders

Details Finding Exponential Product Formulas of Higher Orders Finding Exponential Product Formulas of Higher Orders

2005-06-02

arxiv.org/abs/math-ph/0506007v1

"Quantum Annealing and Other Optimization Methods," Eds. A. Das and B.K. Chakrabarti (Springer, Berlin, 2005) pp. 37-68

Physics

Mathematical Physics

22 pages, 9 figures. To be published in the conference proceedings ''Quantum Annealing and Other Optimization Methods," eds. B

Scientific paper

10.1007/11526216_2

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.

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