"Entanglement" is the black box there, and PCT, as set out in the materials I've linked to in past posts, is the general form the real answer will take.
The more general answer, but too general to be of practical use, is the one that several people have given already. At some point the hardware bottoms out in doing the task instead of thinking about it.
Here's our place to discuss Less Wrong topics that have not appeared in recent posts. Have fun building smaller brains inside of your brains (or not, as you please).