  Adiabatic transport provides a powerful way to manipulate quantum states. By
preparing a system in a readily initialised state and then slowly changing its
Hamiltonian, one may achieve quantum states that would otherwise be
inaccessible. Moreover, a judicious choice of final Hamiltonian whose
groundstate encodes the solution to a problem allows adiabatic transport to be
used for universal quantum computation. However, the dephasing effects of the
environment limit the quantum correlations that an open system can support and
degrade the power of such adiabatic computation. We quantify this effect by
allowing the system to evolve over a restricted set of quantum states,
providing a link between physically inspired classical optimisation algorithms
and quantum adiabatic optimisation. This new perspective allows us to develop
benchmarks to bound the quantum correlations harnessed by an adiabatic
computation. We apply these to the D-Wave Vesuvius machine with revealing -
though inconclusive - results.
