A fine post at the Physics and Cake blog got me thinking about computronium and how it might be realized in M-theory. Of course, this is a purely theoretical musing, but nevertheless is worthy of some consideration. For surely any advanced intelligent civilization, who have already solved M-theory will necessarily develop advanced technology that makes use of quantum gravity and its higher dimensional physics. This will especially be the case in the area of computational technology. So, using M-theory, what form might such computational technology take? Is there an M-theoretical computronium? If so, how do we program it?
Surely, the ultimate computronium is the quantum vacuum itself. Along these lines, in a string/M-theory context, by invoking the correspondence between black holes and qubits, one can see hints as to how the vacuum might eventually serve as a computational substrate. See, for example:
In M-theory, there exist stable non-perturbative states (BPS states) with mass equal to a fraction of the supersymmetry central charge. These states arise from configurations of two and five-dimensional branes, gravitational waves and Taub-NUT-like monopoles. (Note there are no superstrings in M-theory. They arise from compactifications of M-branes in dimensional reduction from D=11 to D=10).
The black hole/qubit correspondence so far has made use of toroidal compactifications of M-theory. That is, one begins with the full 11-dimensions of M-theory and starts to curl up dimensions so that n of them form a higher-dimensional torus (doughnut shape), T^n. This then describes a lower dimensional supergravity theory, in D-n dimensions.
In the D-n dimensional supergravity theory, some BPS states arising from configurations in M-theory behave like microscopic black holes. These black holes are called extremal black holes, as they can be thought of as the ground states of black holes undergoing Hawking radiation. These states have no analog in general relativity, but do exist in supergravity and M-theory which consider quantum effects.
So far what has been found is that in M-theory compactifications down to dimensions D=3,4,5,6, BPS black hole solutions behave like entangled qubits and qutrits. More precisely, the invariants used to classify black holes with different fractions of supersymmetry, end up being the same invariants used to classify entanglement classes of qubits and qutrits. Even more, the black hole mathematical techniques classify qubits and qutrits over not only the real and complex numbers, but over higher dimensional division algebras in four and eight dimensions. So string theory actually predicts new types of qubits and qutrits and classifies their entanglement classes in advance.
Now, in practice, if M-theory is correct, the vacuum should be teeming with such microscopic black holes. They would, in a sense, serve as the qudits of an M-theoretical computronium. Specific types of transformations in M-theory called U-duality transformations, that map between BPS black hole solutions, would then serve as ‘quantum gates’ for these qudits.
Hence, to tell the M-theory vacuum what we would like to do, amounts to the programming of microscopic black holes via U-duality machine code.