I read these two posts and now I am more confused.

Do heavier objects fall faster?

Don&#39;t heavier objects actually fall faster because they exert their own gravity?

I was going to ask: if mass is an objects tendency to resist acceleration then why do two objects of different masses fall to the Earth at the same acceleration?

Then I read those posts and it seems that even though it is very small, the more massive object falls faster. Okay I understand, both objects attract each other.

If two cars of different masses collide doesn't the car with less mass accelerate more even though both cars received the same Force. Then that implies you need more force to accelerate a large mass than to accelerate a small mass. Because that is how I see it, the Moon attracts the Earth with the same Force as the Earth attracts the Moon but the Earth accelerates less due to its larger mass.

So then how is mass an object's tendency to resist acceleration? I am aware of $F_1 = F_2 = GMm/r^2$. So should we not really be able to see the difference in acceleration when dropping a massive object?


Question: How is the energy/eigenvalue gap plot drawn for adiabatic quantum computation?
Answer: The latter. The reason is because it doesn't make a lot of sense to do the eigendecomposition of an approximated Hamiltonian, which is what you're doing when solving for the dynamics (your operator probably won't be Hermitian so your energies won't even be real). Doing the evolution gives you the final state probabilities, but it's not very good for analyzing the energy gap precisely.

So you just plug in the right $s$ values and find the eigenvalues of that $H(s)$, and plotting that gives you the eigenspectrum in Fig. 1.