[rwallace]

Be careful: there's an important distinction. There is a consensus that quantum computers can, for certain problems, perform computation exponential in the number of qubits. But the often unspoken assumption is that the difficulty of getting the computation to stay coherent, is polynomial in the number of qubits. That's currently the big unknown. If it's not, then that's what would be meant by practical quantum computers being physically impossible.

[OscarCunningham]

Is that not the problem that the threshold theorem solves?

[rwallace]

As I understand it (disclaimer: not a physicist), that's the open question: does there exist a stable configuration of atoms that will create conditions such that the threshold theory applies in full, errors are adequately corrected, and an N-qubit quantum computer can be built and operated for cost polynomial rather than exponential in N? Or does that line of thinking rely on assumptions that can't actually be met?