Exponentially Improved Product Formulae using Extrapolation

Product formulas are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance, which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolation have been proposed to mitigate the Trotter error incurred by the use of these formulas. We show these techniques can achieve exponentially better scaling in the error parameter for both randomised and deterministic product formulae.