In a lecture, recorded on Youtube, Gil Kalai presents a 'deduction' for why topological quantum computers will not work. The interesting part is that he claims this is a stronger argument than the argument against fault tolerant computing in general.
If I understand his argument correctly, he states that
A (hypothetical) quantum computer without quantum error correction can simulate the system of anyons representing the qubit in a topological quantum computer.
Therefore, any quantum computer based on these anyons must have at least as much noise as a quantum computer without quantum error correction. As we know that our noisy quantum computer is insufficient for universal quantum computation, topological quantum computers based on anyons cannot provide universal quantum computation either.
I think step 2 is sound, but I have some doubts on step 1 and why it implies 2. In particular:
- Why can a quantum computer without error correction simulate the system of anyons?
- If it can simulate the system of anyons, is it possible that it can only do so with low probability and hence cannot simulate the topological quantum computer with the same fault tolerance as the system of anyons?