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l2718 comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 113 - Less Wrong Discussion
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This is not quite phrased correctly. While I know less magic than the protagonist (having not attended Hogwarts for a year), I know far more physics and mathematics than he does. I am also privy to world-building knowledge that he isn't. For example, we know about major artefacts:
We also know little trivia:
In conclusion: it's not enough for us to think of a solution, we also need to explain how Harry can think of it. There's no point in simulating Harry's smarts on my hardware, I can use my own smarts. But I do need to simulate Harry's knowledge.
Similarly, it would be seriously pushing it to rely on any scientific advances of the last (real-world) decade or so, unless there's a reason Harry would be able to at least semi-plausibly pre-discover them himself. Not that I can think of any of those which would help anyhow, but it's something to keep in mind.
Future tech - even things we think we could perhaps do - is probably right out. Harry could conceivably transfigure something (his epidermis, for example; has anybody mentioned that yet?) into a material that we know exists or could exist, and can describe in atomic or sub-atomic detail, yet can't synthesize; an arbitrary isotope of an arbitrary element should probably be possible, for example. He can't use transfiguration to produce something with negative mass (http://en.wikipedia.org/wiki/Negative_mass), though... at least, I would assume not, even if the science he knows suggests that such a thing is theoretically possible.