Is there a geometrical picture for adiabatic quantum computation?
a very challenging/advanced/provocative question; following, a brief/sketchy/tentative answer [maybe/hopefully better than none] considering geometry in QM computing in general &amp; a few refs/leads. geometry is used in a variety of ways in QM in general, and it appears to be somewhat of an open question and challenging work-in-progress how to determine a coherent/natural "geometric picture" for QM, and there apparently are multiple ways to do it, and currently no generally-agreed, unified or standard approach. also, some directions can be highly abstract reflecting the direction of mathematical research developed largely independently of physics.

the 2-qubit state has been more extensively studied and there is more chance of creating a picture there 1st and maybe using it as a somewhat "toy" area that can be expanded later. (note that adiabatic QM computing is still based on qubits.) also there is a relatively new study of "quantum dischord" which is seen as promising by some (but also controversial) &amp; might be part of the answer as in the following ref.


the Bloch sphere is a clear geometric picture for a single qubit and has some generalization for pure states.
Geometric picture of quantum discord for two-qubit quantum states Shi, Jiang, Sun, Du
Geometry of Discrete Quantum Computing Hanson, Ortiz, Sabry, Tai
Quantum computing: The power of discord Merali/Nature