[onetimeuse92304]

Even if the universe is infinite, you can't use its infiniteness because you can't communicate partial results across infinite distances.

It is natural to think that the more time you have, the further you can travel to, potentially. But when it comes to the universe, the opposite is actually true. The more time passes, the less of the universe you can reach. A lot of universe you can see today is actually not at all reachable, meaning even if you shine the light back it will never reach the destination.

[smaudet]

Computational capacity must not be able to travel faster than the speed of light, yes?

We are told that quantum entanglement cannot transmit information, I am unaware of how rigorously this has been proven/disproven, on the off chance there is something the scientists have missed, the requirement to travel might not be necessary. Either through some advanced entanglement (a novel approach or a not yet understood state of matter), or reaching for a more exotic theory, some additional dimension enabling warp or wormhole like behaviors.

Then computational capacity would depend on some ratio of power (to entangle, set up facilities, etc.) to time spent not doing these things, and might possibly have an upper limit, or not. Perhaps this is a halting problem in itself?

[eigenket]

> We are told that quantum entanglement cannot transmit information, I am unaware of how rigorously this has been proven/disproven

This has been rigorously proven [1]. If you are transmitting information you are doing something in addition to using entanglement.

[1] https://en.wikipedia.org/wiki/No-communication_theorem

[danbruc]

Only because our universe is currently expanding, if it wasn't or would stop in the future, given enough time you could eventually distribute the task over a large enough region to perform the computation and afterwards combine the results in one place. And one would probably have to throw in a couple of technical requirements, for example that the energy density does not decrease faster than the future light cone expands.