  Understanding how non-adiabatic terms affect quantum dynamics is fundamental
to improving various protocols for quantum technologies. We present a novel
approach to computing the Adiabatic Gauge Potential (AGP), which gives
information on the non-adiabatic terms that arise from time dependence in the
Hamiltonian. Our approach uses commutators of the Hamiltonian to build up an
appropriate basis of the AGP, which can be easily truncated to give an
approximate form when the exact result is intractable. We use this approach to
study the AGP obtained for the transverse field Ising model on a variety of
graphs, showing how the different underlying graph structures can give rise to
very different scaling for the number of terms required in the AGP.
