The quantum adiabatic algorithm solves problems by evolving a known initial state towards the ground state of a Hamiltonian encoding the answer to a problem. Although continuous- and discrete-time quantum algorithms exist capable of evaluating tree graphs consisting of N vertexes in $$O(\sqrt{N})$$ O ( N ) time, a quadratic improvement over their classical counterparts, no quantum adiabatic procedure is known to exist. In this work, we present a study of the main issues and challenges surrounding quantum adiabatic evaluation of NAND trees. We focus on a number of issues ranging from: (1) mapping mechanisms; (2) spectrum analysis and remapping; (3) numerical evaluation of spectrum gaps; and (4) algorithmic procedures. These concepts are then used to provide numerical evidence for the existence of a $$\frac{N^{2}}{\log {N^{2}}}$$ N 2 log N 2 gap.