  A major challenge facing adiabatic quantum computing is that algorithm design
and error correction can be difficult for adiabatic quantum computing. Recent
work has considered addressing his challenge by using coherently controlled
adiabatic evolutions in the place of classically controlled evolution. An
important question remains: what is the relative power of controlled adiabatic
evolution to traditional adiabatic evolutions? We address this by showing that
coherent control and measurement provides a way to average different adiabatic
evolutions in ways that cause their diabatic errors to cancel, allowing for
adiabatic evolutions to combine the best characteristics of existing adiabatic
optimizations strategies that are mutually exclusive in conventional adiabatic
QIP. This result shows that coherent control and measurement can provide
advantages for adiabatic state preparation. We also provide upper bounds on the
complexity of simulating such evolutions on a circuit based quantum computer
and provide sufficiency conditions for the equivalence of controlled adiabatic
evolutions to adiabatic quantum computing.
