I'm not sure whether this question is completely on-topic, since it is a physics-related question. But I'll ask anyway and apologize if I'm off-topic.
In Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation the autors mention a tradeoff between runtime and energy:
"Observe that we have chosen our definition of running time to be $T · \max_s \lVert H(s)\rVert$ and not T. Notice that if the Hamiltonians are multiplied by some factor, this divides the bound of Equation 2, and hence T, by the same factor. Hence, if the running time is defined to be T one would be able to achieve arbitrarily small running times, by multiplying the Hamiltonians by large factors. Our definition, on the other hand, is invariant under a multiplication of the Hamiltonian by an overall factor, and so takes into account the known physical trade-off between time and energy.5
5This trade-off between time and the norm of the Hamiltonian (namely, the energy), is manifested in Schrödinger’s equation whose solution does not change if time is divided by some factor and at the same time the Hamiltonian is multiplied by the same factor."
But if I understand correctly, adiabatic quantum computation is completely reversible: by inverting the direction of time the system evolves back from the final state to the initial state.
Moreover, any adiabatic quantum computation process can be implemented (with arbitrary precision) in the conventional quantum circuit model, where all the gates are unitary and thus reversible.
According to Landauer's principle, reversible computation could be, in principle, executed without any energy consumption.
So my question is, what exactly the time-energy tradeoff in the choice of Hamiltonians for adiabatic quantum computation means?