Optimal-order Trotter-Suzuki decomposition for quantum simulation on noisy quantum computers

Abstract: 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.