  One of the goals in quantum simulation is to adiabatically generate the
ground state of a complicated Hamiltonian by starting with the ground state of
a simple Hamiltonian and slowly evolving the system to the complicated one. If
the evolution is adiabatic and the initial and final ground states are
connected due to having the same symmetry, then the simulation will be
successful. But in most experiments, adiabatic simulation is not possible
because it would take too long, and the system has some level of diabatic
excitation. In this work, we quantify the extent of the diabatic excitation
even if we do not know {\it a priori} what the complicated ground state is.
Since many quantum simulator platforms, like trapped ions, can measure the
probabilities to be in a product state, we describe techniques that can employ
these measurements to estimate the probability of being in the ground state of
the system after the diabatic evolution. These techniques do not require one to
know any properties about the Hamiltonian itself, nor to calculate its
eigenstate properties. All the information is derived by analyzing the
product-state measurements as functions of time.
