2005/06/02 by Naomichi Hatano, Masuo Suzuki · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Numerical methods for differential equations #Quantum Computing Algorithms and Architecture #Quantum chaos and dynamical systems #cond-mat.stat-mech #math-ph #math.MP #msc:41A35 #msc:65P10 #msc:82C80 #physics.comp-ph #quant-ph
paper · pdf · doi:10.1007/11526216_2
published as "Quantum Annealing and Other Optimization Methods," Eds. A. Das and B.K. Chakrabarti (Springer, Berlin, 2005) pp. 37-68 · 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)
arxiv created 2005/06/02 · openalex publication_date 2005/11/16 · arxiv updated 2011/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.