Higher Order Decompositions of Ordered Operator Exponentials
  We present a decomposition scheme based on Lie-Trotter-Suzuki product formulae to represent an ordered operator exponential as a product of ordinary operator exponentials. We provide a rigorous proof that does not use a time-displacement superoperator, and can be applied to non-analytic functions. Our proof provides explicit bounds on the error and includes cases where the functions are not infinitely differentiable. We show that Lie-Trotter-Suzuki product formulae can still be used for functions that are not infinitely differentiable, but that arbitrary order scaling may not be achieved. 
Nathan Wiebe (U Calgary), Dominic W. Berry (Macquarie University),   Peter Hoyer (U Calgary), Barry C. Sanders (U Calgary)