To efficiently implement many-particle quantum simulations on quantum computers we develop and present methods for inverting the Campbell-Baker-Hausdorff lemma to 3rd and 4th order in the commutator. That is, we reexpress exp{-i(H_1 + H_2 + ...)dt} as a product of factors exp(-i H_1 dt), exp(-i H_2 dt), ... which is accurate to 3rd or 4th order in dt.
@article{arxiv.quant-ph/9809009,
title = {Higher-Order Methods for Quantum Simulations},
author = {A. T. Sornborger and E. D. Stewart},
journal= {arXiv preprint arXiv:quant-ph/9809009},
year = {2007}
}