  The simulation of time evolution of large quantum systems is a classically
challenging and in general intractable task, making it a promising application
for quantum computation. A Trotter-Suzuki approximation yields an
implementation thereof, where a higher approximation accuracy can be traded for
an increased gate count. In this work, we introduce a variational algorithm
which uses solutions of classical optimizations to predict efficient quantum
circuits for time evolution of translationally invariant quantum systems. Our
strategy can improve upon the Trotter-Suzuki accuracy by several orders of
magnitude. It translates into a reduction in gate count and hence gain in
overall fidelity at the same algorithmic accuracy. This is important in
NISQ-applications where the fidelity of the output state decays exponentially
with the number of gates. The performance advantage of our classical assisted
strategy can be extended to open boundaries with translational symmetry in the
bulk. We can extrapolate our method to beyond classically simulatable system
sizes, maintaining its total fidelity advantage over a Trotter-Suzuki
approximation making it an interesting candidate for beyond classical time
evolution.
