A quantum processor, taking advantage of the qubit mutual superposition effects, should be able to solve O(n²) problems per single clock tick. Likewise, the universe -made up of quantum particles- should have the same computing power, being n the number of particles in the whole universe.

Nonetheless, aside from collapses, there is a fixed limit: the speed of light times distance. That means, two close atoms would process faster than two atoms with a light year between them.

More precisely, the top speed would be given by the number of possible collapses per second times the maximum distance in light seconds between the qubits involved in a given processor.

A fractal system which would use the fact that closer particles process faster, could actually process ¡faster than the universe!

At least at the level of problems not requiring more than a number of qubits divided by the simplification factor of whatever we would like to process. No quantum computer could possibly process the whole universe, as every next particle would require a n+1 higher complexity. Although, it would be an interesting experiment to calculate the possibility of calculating a simplified universe on a lower amount of particles. How much would the speed of light influence it? How bigger would be the increase than the decrease due to resolution?

The interesting part, though, is that with relatively small processors and a level of multiple abstraction good enough, it should be easily possible to simulate slices of reality big enough so the collapses would not differ much from those observed in the real world by those who live in it.

Compressed worlds, accelerated even though at a lower resolution. Would be like to live in them? The speed of light would be no obstacle, given that only the distance between simulating particles would matter, not the simulated ones. Even losing a big amount of resolution in the simulation process, it surely would be quite an interesting place.

But everything poses dangers -and not only social ones- as to much distance reduction could lead to, a black hole!

We think that inside a black hole, relativistic equations should be maintained, so from the point of view of a world simulated by particles in a black hole, there would be no speed increase; it would always be the same.

Will it be our future, to become a phantom world inside a black hole, with no possibility whatsoever to go back and escape the reality we would impose on ourselves?

Or, maybe, the evaporation effect would come to the rescue, letting us extract information from nano-scale black holes, making with them quantum processors at the highest possible speed.

Really, right now I would be glad to have a quantum processor with a few million qubits, if possible running at a few gigaflops, to solve a cool O(n³) problem I have in mind. Maybe in the next decade, the world of programming will be quite different.