Error Estimates and Higher Order Trotter Product Formulas in Jordan-Banach Algebras
Abstract
In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this paper, we extend the analysis of Trotter-Suzuki approximations, including third and higher orders, to Jordan-Banach algebras. We solve an open problem in our earlier paper on the existence of second-order Trotter formula error estimation in Jordan-Banach algebras. To illustrate our work, we apply our formula to simulate Trotter-factorized spins, and show improvements in the approximations. Our approach demonstrates the adaptability of Trotter product formulas and estimates to non-associative settings, which offers new insights into the applications of Jordan algebra theory to operator dynamics.
Cite
@article{arxiv.2412.20604,
title = {Error Estimates and Higher Order Trotter Product Formulas in Jordan-Banach Algebras},
author = {Sarah Chehade and Andrea Delgado and Shuzhou Wang and Zhenhua Wang},
journal= {arXiv preprint arXiv:2412.20604},
year = {2025}
}