Improved Quantum Computing with the Higher-order Trotter Decomposition

It is crucial to simulate the controlled system evolution on a classical computer for designing precise quantum control. However, computing the time evolution operator is resource-consuming, especially when the total Hamiltonian is not allowed to diagonalize. In this work, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering (GRAPE) algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient ansatzes for the variational quantum algorithm (VQA), leading to improved performance on solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks.