  We perform exact diagonalization and time evolution of the
Lechner-Hauke-Zoller (LHZ) annealing architecture [Science Advances 1(9),
e1500838 (2015)] for ten physical qubits. Thereby, on a training set consisting
of $2400$ problem instances, we perform the optimization task of tuning the
local fields with the goal to identify a set of fixed optimal annealing
protocols, that outperforms linear protocols on a large class of arbitrary LHZ
problem instances. We show that average ground state fidelities of $0.9$ can be
achieved by applying optimized protocols onto groups of problem instances with
similar energy landscapes. Particularly, the set of optimized annealing
protocols reduces annealing time required to reach a predefined threshold
ground state fidelity by an average of $\sim72\%$, corresponding to a speed-up
of factor $\sim3.5$. Moreover, as these protocols are meant to be readily
applicable in experimental setups, they can be used as a starting point for
problem-specific protocol optimization. In reverse, we discuss how previously
optimized protocols can potentially be used to gauge the instantaneous energy
landscape of a spin glass problem. Albeit simulations were performed on the LHZ
architecture, identification of optimized protocols is not limited to either
simulations or local connectivity only.
