Optimize quantum simulation using a force-gradient integrator

Quantum simulation has shown great potential in many fields due to its powerful computational capabilities. However, the limited fidelity can lead to a severe limitation on the number of gate operations, which requires us to find optimized algorithms. Trotter decomposition and high order Trotter decompositions are widely used in quantum simulations. We find that they can be significantly improved by force-gradient integrator in lattice QCD. By using two applications as examples, we show that the force-gradient decomposition can reduce the number of gate operations up to about a third of those using high order Trotter decompositions. Therefore, force-gradient decomposition shows a great prospective in future applications of quantum simulation.