From a mathematical point of view, it seems to me that our understanding of how the complexity of quantum systems scales with size. For example, it's easier to build $n$ $1$-qubit computers than one $n$-qubit computer. In my mind, this is roughly analogous to the fact that it's easier to solve $n$ $1$-body problems than one $n$-body problem, since entanglement is the primary motivating factor behind quantum computing in the first place.

My question is the following: It seems that we should really care about how the 'difficulty' of controlling an $n$-body quantum system grows with $n$. Here difficulty could be defined in any number of ways, and the question we would care about, roughly is, is controlling a $1000$-qubit machine 'merely' 100x harder than controlling a $10$-qubit machine, or $100^2$, or $100!$ or $100^{100}$? Do we have any reasons for believing that it is more or less the former, and not the latter?