“If we now consider what it means to perform a quantum computation in such a situation, we apparently come to the conclusion that non-computable operations can be performed! This arises from the fact that in the space-time geometries with closed timelike lines, a Turing-machine operation can feed on to its own output, running around indefinitely, if necessary, so that the answer to the question 'does that computation ever stop' has an actual influence on the final result of the quantum computation. Deutsch comes to the conclusion that in his quantum gravity scheme, quantum oracle machines are possible. As far as I can make out, his arguments would apply just as well to higher-order oracle machines also.

Of course, many readers may feel that all this should be taken with an appropriate amount of salt. Indeed, there is no real suggestion that the scheme provides us with a consistent (or even plausible) theory of quantum gravity. Nonetheless, the ideas are logical within their own framework and are suggestively interesting-and it seems quite reasonable to me that when the appropriate scheme for quantum gravity is eventually found, then some important vestiges of Deutsch's proposal will indeed survive.”