We construct product formulas of orders 3 to 6 approximating the exponential of a commutator of two arbitrary operators in terms of the exponentials of the operators involved. The new schemes require a reduced number of exponentials and thus provide more efficient approximations than other previously published alternatives, whereas they can be still used as a starting methods of recursive procedures to increase the order of approximation.

翻译：我们构建了3至6阶的乘积公式，用于通过涉及算子的指数来逼近两个任意算子交换子的指数。新方案所需的指数数量减少，因此提供了比先前发表的其他方法更高效的逼近，同时仍可作为递归过程的起始方法以提高逼近阶数。