  Variational quantum time evolution allows us to simulate the time dynamics of
quantum systems with near-term compatible quantum circuits. Due to the
variational nature of this method the accuracy of the simulation is a priori
unknown. We derive global phase agnostic error bounds for the state simulation
accuracy with variational quantum time evolution that improve the tightness of
fidelity estimates over existing error bounds. These analysis tools are
practically crucial for assessing the quality of the simulation and making
informed choices about simulation hyper-parameters. The efficient, a posteriori
evaluation of the bounds can be tightly integrated with the variational time
simulation and, hence, results in a minor resource overhead which is governed
by the system's energy variance. The performance of the novel error bounds is
demonstrated on numerical examples.
