A visual introduction to big O notation

What blows me away is that there are quantum calculations which grow as O**7 with respect to the number of atoms and scientists are fine with running them because N is small, computers get faster and more memory all the time, and the results are valuable.

(I'm not a computer science expert, so if I used the O(n) terminology differently from the standard, sorry).

You can simply say grows as n⁷. Although people will understand what you mean by saying O(n⁷), O is an upper bound, not a lower bound.

What you should say if you want to be correct is it grows as Ω(n⁷).

"Fine with running them" is a bit of a stretch, though the gist is correct.

There's a whole hierarchy of quantum chemistry algorithms where accuracy is traded with asymptotic runtime, I think starting at N*^3 and going all the way to N!.