Classical Variational Optimization of Gate Sequences for Time Evolution of Translational Invariant Systems

The simulation of time evolution of large quantum systems is a classically challenging and often intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation thereof, where a certain desired accuracy can be achieved by raising the gate count adequately. In this work, we introduce a variational algorithm which uses solutions of classical optimizations to predict efficient quantum circuits for time evolution of translational invariant quantum systems. Our strategy improves on the Trotter-Suzuki ansatz in accuracy by several orders of magnitude. Alternatively, one can trade the accuracy gain against a reduction of gate count. This is important in NISQ-applications where the fidelity of the output state decays exponentially with the number of gates. We also propose an extension of our strategy to construct algorithms for the evolution of open boundary systems with translation symmetry in the bulk.