Problem-specific classical optimization of Hamiltonian simulation

Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and sampling problems. Here, we present a classical preprocessing routine for variational Hamiltonian simulation that circumvents the need for a quantum optimization by expanding rigorous error bounds in a perturbative regime for suitable time steps. The resulting cost function is efficiently computable on a classical computer. We show that there always exists potential for optimization with respect to a Trotter sequence of the same order and that the cost value has the same scaling as Trotter in simulation time and system size. Unlike previous work on classical preprocessing, the method is applicable to any Hamiltonian system independent of locality and interaction lengths. Via numerical experiments for spin-lattice models, we find that our approach significantly improves digital quantum simulation capabilities with respect to Trotter sequences for the same resources. For short times, we find accuracy improvements of more than three orders of magnitude for our method as compared to Trotter sequences of the same gate number. Moreover, for a given gate number and accuracy target, we find that the preoptimization we introduce enables simulation times that are consistently more than ten times longer for a target accuracy of 0.1%.