Error bounds for variational quantum time evolution

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 a posteriori global phase agnostic error bounds for the state simulation accuracy with variational quantum time evolution that improve the tightness of fidelity estimates over existing a posteriori error bounds. These analysis tools are practically crucial for assessing the quality of the simulation and making informed choices about simulation hyperparameters. 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 error bounds is demonstrated on numerical examples.