[dalke]

O(n3) for classical MM? Electrostatics is O(n2) and with multipole methods it's less than that. What's O(n3) about MM?

[PhysicsAndYou]

One of many typos unfortunately.

Keeping track of everything explicitly its n^2.

Also it really, really depends on the level of theory for the scaling of quantum regions/algorithms. To say at minimum O(n^5) is incorrect.