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Digital quantum simulation is a promising application of quantum computers,where quantum dynamics is simulated by using quantum gate operations. Manytechniques for decomposing a time-evolution operator of quantum dynamics intosimulatable quantum gate operations have been proposed, while these methodscause some errors. To evaluate these errors, we derive a lower bound foroverlap between true dynamics and digital simulated dynamics at the final time.Our result enables us to guarantee how obtained digital simulated dynamics isclose to unknown true dynamics. We also extend our formalism to errorevaluation of digital quantum simulation on noisy quantum computers.

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