  The potential of employing higher orders of the Trotter-Suzuki decomposition
of the evolution operator for more effective simulations of quantum systems on
a noisy quantum computer is explored. By examining the transverse-field Ising
model and the XY model, it is demonstrated that when the gate error is
decreased by approximately an order of magnitude relative to typical modern
values, higher-order Trotterization becomes advantageous. This form of
Trotterization yields a global minimum of the overall simulation error,
comprising both the mathematical error of Trotterization and the physical error
arising from gate execution.
