  The Trotter-Suzuki decomposition is an important tool for the simulation and
control of physical systems. We provide evidence for the stability of the
Trotter-Suzuki decomposition. We model the error in the decomposition and
determine sufficiency conditions that guarantee the stability of this
decomposition under this model. We relate these sufficiency conditions to
precision limitations of computing and control in both classical and quantum
cases. Furthermore we show that bounded-error Trotter-Suzuki decomposition can
be achieved by a suitable choice of machine precision.
