The construct is a complexity class, meaning that it is a set of problems which can be[1] solved by quantum computers[2] in a reasonable[3] time. Those three aspects correspond to words which get initialized as the name of this complexity class -- BQP, bounded-error quantum polynomial-time.
Aaronson's proof involves an observation that PostBQP = PP, in other words, all of the problems you can solve with an especially powerful quantum computer can also be solved with an even more especially powerful classical computer, and vice versa. Since the quantum computer is easier to reason about, you get a hard result as a freebie.
BQP is not a tongue-in-cheek thing; it's also not a well-understood thing -- just "anything which quantum computers can do in this way quickly with bounded errors" -- but it's certainly better understood than this amplituhedron is. The real problem he's highlighting is that complexity classes like BQP have scary names.
For the sake of this discussion, you can imagine a similar problem with "programmable imperative syntax" and "monads". Really all that monads are, in a computing context, is a way of formalizing a programmable imperative syntax as a purely functional programming construct. The issue is that when you say "functional" and "monads" then people kind of just shut down, they don't want to hear about it. Does that make sense?
Comments
The construct is a complexity class, meaning that it is a set of problems which can be[1] solved by quantum computers[2] in a reasonable[3] time. Those three aspects correspond to words which get initialized as the name of this complexity class -- BQP, bounded-error quantum polynomial-time.
Aaronson's proof involves an observation that PostBQP = PP, in other words, all of the problems you can solve with an especially powerful quantum computer can also be solved with an even more especially powerful classical computer, and vice versa. Since the quantum computer is easier to reason about, you get a hard result as a freebie.
BQP is not a tongue-in-cheek thing; it's also not a well-understood thing -- just "anything which quantum computers can do in this way quickly with bounded errors" -- but it's certainly better understood than this amplituhedron is. The real problem he's highlighting is that complexity classes like BQP have scary names.
For the sake of this discussion, you can imagine a similar problem with "programmable imperative syntax" and "monads". Really all that monads are, in a computing context, is a way of formalizing a programmable imperative syntax as a purely functional programming construct. The issue is that when you say "functional" and "monads" then people kind of just shut down, they don't want to hear about it. Does that make sense?