3 ms·
I should have said the "strong" Church-Turing thesis, which is a statement about efficiency: anything that can be computed efficiently can be computed efficient
by j2kun 13y ago
I should have said the "strong" Church-Turing thesis, which is a statement about efficiency: anything that can be computed efficiently can be computed efficiently by a Turing machine. In other words, if quantum computers can solve problems in polynomial time that classical computers cannot, then the strong Church-Turing thesis is false. The normal Church-Turing thesis, which just says that anything which can be computed can be computed by a Turing machine, is still true when you consider quantum circuits: Turing machines can simulate quantum computers just fine if you are happy to wait a long time.
That being said, there could very well be models of computing (based on weird physical phenomena) that violate one or both versions of the Church-Turing thesis. Scott has expressed a few times that the possibility intrigues him, though I don't know whether he would bet his life's fortune on one outcome or the other :)