Experimental Performance of a Quantum Simulator: Optimizing Adiabatic Evolution and Identifying Many-Body Ground States

We use local adiabatic evolution to experimentally create and determine the
ground state spin ordering of a fully-connected Ising model with up to 14
spins. Local adiabatic evolution -- in which the system evolution rate is a
function of the instantaneous energy gap -- is found to maximize the ground
state probability compared with other adiabatic methods while only requiring
knowledge of the lowest $\sim N$ of the $2^N$ Hamiltonian eigenvalues. We also
demonstrate that the ground state ordering can be experimentally identified as
the most probable of all possible spin configurations, even when the evolution
is highly non-adiabatic.