They are meant to be arbitrarily accurate, and so we would expect them to include qualia.

Whose "we"? They are only mean to be functional (input-output) duplicates, and a large chunk of the problem of qualiia is that qualia are not in any remotely obvious way functions.

However, in the Chalmers vein consciousness is non-physical, which suggests it cannot be simulated through physical means.

If you think consciousness is non physical , you would think the sims are probably zombies. You would also think that if you are a physicalist but not a computationalist. Physicalism does not guarantee anything about the nature of computational simulations.

Chalmers actual position is that consciousness supervenes on certain kinds of information processing, so that a sufficiently detailed simulation would be conscious: he's one of the "we".