The full t’ ‘t Hooft (look I put the apostrophy in the correct location!) article is now posted at Physics World (not Physics Today, as I listed incorrectly in my first post) commentary by Edward Witten, Fay Dowker, and Paul Davies. Quick summary: Witten thinks that quantum cosmology is perplexing, Dowker worries about the emergence of classical physics, and Davies postulates that complexity is the key to understanding the emergence of classicality. Davies suggests that quantum mechanics will break down when the Hilbert space is of size 10^120 and suggests that quantum comptuers will fail at this size. His argument could equally be applied to probablistic classical computers, and so I suggest that if he is right, then classical computers using randomness cannot be any larger than 400 bits.
O brave new quantum world!
So how many components are in current 1 or 2 qubit quantum computers?
Actually, I think you’ve made a mistake. Davies says 10^120 bits, not states. So it should be 2^(10^120), not 10^120, states. (Which corresponds to a rather larger Hilbert space).
Actually, I see where that number comes from in the article, but it seems inconsistent with his earlier remark about 10^120 bits.
Heh. Yeah Davies has taken the number of bits 10^120 and stated that “quantum mechanics will break down when the dimensionality of the Hilbert space exceeds about 10^120.” I wonder what he would say about Holevo’s theorem?
It seems a ridiculous mistake to make. Its equivalent to saying that N qubits have a 2N dimensional Hilbert space.
It also occurs to me that the Hilbert space for a harmonic oscillator exceeds this limit, and so by his reasoning, you shouldn’t be able to treat them, or any continuous variable system, exactly using quantum mechanics.
I’m clearly preaching to the choir here, but Davies’ closing line “If my ideas are right, then this eagerly awaited technology will never achieve its full promise.” is obviously absurd.
If his ideas were right, then quantum computers would expose a flaw in quantum theory, which would be much more exciting than factoring.