In order to do the X-basis measurement described in the paper, it's necessary to do very funky things to the simulated agents inside the computers. Probably the easiest way to implement the measurement would be to literally rewind the simulation back to before the measurement started, when the superposition was limited to a single qubit, do the measurement at that time, and then run the simulation back forwards to the current time. The paper doesn't specify an implementation, so it should work for any implementation, so this should be a valid way of doing the operation. But this implementation implies you're undoing all the reasoning the agents did, changing the initial state, and so as you run them forwards again they are redoing the same reasoning steps but in a new context where the premises no longer apply. Which of course results in them making mistakes. The same thing would happen classically, if you rewound a simulated agent to change some crucial fact and then assumed reasoning from premises that no longer held should still be valid.
I think Scott also co-authored a follow up paper, where they made some steps towards proving that the only computationally efficient way to implement the X-basis measurement was to do this simulation rewinding thing. But unfortunately I can't seem to find it now.
Strilanc|7 months ago
In order to do the X-basis measurement described in the paper, it's necessary to do very funky things to the simulated agents inside the computers. Probably the easiest way to implement the measurement would be to literally rewind the simulation back to before the measurement started, when the superposition was limited to a single qubit, do the measurement at that time, and then run the simulation back forwards to the current time. The paper doesn't specify an implementation, so it should work for any implementation, so this should be a valid way of doing the operation. But this implementation implies you're undoing all the reasoning the agents did, changing the initial state, and so as you run them forwards again they are redoing the same reasoning steps but in a new context where the premises no longer apply. Which of course results in them making mistakes. The same thing would happen classically, if you rewound a simulated agent to change some crucial fact and then assumed reasoning from premises that no longer held should still be valid.
I think Scott also co-authored a follow up paper, where they made some steps towards proving that the only computationally efficient way to implement the X-basis measurement was to do this simulation rewinding thing. But unfortunately I can't seem to find it now.