That may be, but such a general point would be about arbitrary qubits or bits, when a simulation doesn’t have to work over all or even most arrangements.
Hmm, so thinking about this more, I think that Holevo’s theorem can probably be interpreted in a way that much more substantially restricts what one would need to know about the other n bits in order to simulate them, especially since one is apparently simulating not just bits but qubits. But I don’t really have a good understanding of this sort of thing at all. Maybe someone who knows more can comment?
Another issue which backs up simulation being easier- if one cares primarily about life forms one doesn’t need a detailed simulation then of the inside of planets and stars. The exact quantum state of every iron atom in the core of the planet for example shouldn’t matter that much. So if one is mainly simulating the surface of a single planet in full detail, or even just the surfaces of a bunch of planets, that’s a lot less computation.
One other issue is that I’m not sure you can have simulations run that much faster than your own physical reality (again assuming that the simulated universe uses the same basic physics as the underlying universe). See for example this paper which shows that most classical algorithms don’t get major speedup from a quantum computer beyond a constant factor. That constant factor could be big, but this is a pretty strong result even before one is talking about general quantum algorithms. Of course, if the external world didn’t quite work the same (say different constants for things like the speed of light) this might not be much of an issue at all.
Hmm, that’s a good point. So it would then come down to how much of an expectation of what the simulation is likely to do do you need in order to get away with using fewer qubits. I don’t have a good intuition for that, but the fact that BQP is likely to be fairly small compared to all of PSPACE suggests to me that one can’t really get that much out of it. But that’s a weak argument. Your remark makes me update in favor of simulationism being more plausible.
That may be, but such a general point would be about arbitrary qubits or bits, when a simulation doesn’t have to work over all or even most arrangements.
Hmm, so thinking about this more, I think that Holevo’s theorem can probably be interpreted in a way that much more substantially restricts what one would need to know about the other n bits in order to simulate them, especially since one is apparently simulating not just bits but qubits. But I don’t really have a good understanding of this sort of thing at all. Maybe someone who knows more can comment?
Another issue which backs up simulation being easier- if one cares primarily about life forms one doesn’t need a detailed simulation then of the inside of planets and stars. The exact quantum state of every iron atom in the core of the planet for example shouldn’t matter that much. So if one is mainly simulating the surface of a single planet in full detail, or even just the surfaces of a bunch of planets, that’s a lot less computation.
One other issue is that I’m not sure you can have simulations run that much faster than your own physical reality (again assuming that the simulated universe uses the same basic physics as the underlying universe). See for example this paper which shows that most classical algorithms don’t get major speedup from a quantum computer beyond a constant factor. That constant factor could be big, but this is a pretty strong result even before one is talking about general quantum algorithms. Of course, if the external world didn’t quite work the same (say different constants for things like the speed of light) this might not be much of an issue at all.
Hmm, that’s a good point. So it would then come down to how much of an expectation of what the simulation is likely to do do you need in order to get away with using fewer qubits. I don’t have a good intuition for that, but the fact that BQP is likely to be fairly small compared to all of PSPACE suggests to me that one can’t really get that much out of it. But that’s a weak argument. Your remark makes me update in favor of simulationism being more plausible.