[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