Return to Question

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?

It seems to me that an extremely relevant question for the prospects of quantum computing would be how the engineering complexity of quantum systems scales with size. Meaning, 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 analytically 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 building and controlling an $n$-body quantum system grows with $n$. Fix a gate architecture, or even an algorithm--is there a difficulty in principle arising from the fact that an $n$-qubit computer is a quantum many-body problem? And that mathematically speaking, our understanding of how quantum phenomena scale up into classical phenomena is quite poor? 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 (that is, preserving the coherence of its wavefunctions) '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 that it is more or less the former, and not the latter?

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?

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?