State-dependent error bound for digital quantum simulation of driven systems

Digital quantum simulation is a promising application of computers where dynamics simulated by using gate operations. Many techniques for decomposing time-evolution operator into simulatable operations have been proposed, whereas these methods cause some errors. To evaluate errors, we derive lower bound overlap between true and digital at the final time. Our result enables us to guarantee how obtained close unknown dynamics. We also extend our formalism error evaluation on noisy computers.