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

Quantum Physics;Statistical Mechanics