Last chapter, we talked about whether quantum states should be thought of as exponentially long vectors, and I brought up class BQP/qpoly and concepts like quantum advice. Actually, I’d say that the main reason why I care is something I didn't mention last time, which is that it relates to whether we should expect quantum computing to be fundamentally possible or not. There are people, like Leonid Levin and Oded Goldreich, who just take it as obvious that quantum computing must be impossible. Part of their argument is that it's extravagant to imagine a world where describing the state of 200 particles takes more bits then there are particles in the universe. To them, this is a clear indication something is going to break down. So part of the reason that I like to study the power of quantum proofs and quantum advice is that it helps us answer the question of whether we really should think of a quantum state as encoding an exponential amount of information.

So, on to the Eleven Objections.

1. Works on paper, not in practice.

2. Violates Extended Church–Turing Thesis.

3. Not enough “real physics.”

4. Small amplitudes are unphysical.

5. Exponentially large states are unphysical.

6. Quantum computers are just souped-up analog computers.

7. Quantum computers aren't like anything we've ever seen before.

8. Quantum mechanics is just an approximation to some deeper theory.

9. Decoherence will always be worse than the fault-tolerance threshold.

10. We don't need fault-tolerance for classical computers.

11. Errors aren't independent.

What I did is to write out every skeptical argument against the possibility of quantum computing that I could think of. We'll just go through them, and make commentary along the way. Let me just start by saying that my point of view has always been rather simple: it's entirely conceivable that quantum computing is impossible for some fundamental reason. If so, then that's by far the most exciting thing that could happen for us. That would be much more interesting than if quantum computing were possible, because it changes our understanding of physics. To have a quantum computer capable of factoring 10000-digit integers is the relatively boring outcome – the outcome that we'd expect based on the theories we already have.