Apologies if this is a naive question--

From a mathematical point of view, it seems to me that our understanding of how complexity of quantum systems scales with size. E.g., it's easier to build $n$ $1$-qubit computers than $1$ $n$-qubit computer. In my mind, this is roughly analogous to the fact that it's easier to solve $n$ $1$-body problems than $1$ $n$-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 is roughly--is controlling a $1,000$-qubit machine 'merely' $100$X harder than controlling a $10$-qubit machine, or $100^2$, or $100!$ or $100^{100}$? Do we have any reasons for believing it is more or less the former, and not the latter?