A great read. My own obscene note would be nature ain't classical, these classical conjectures are all "unnatural", the quantum versions should be the focus ;)https://twitter.com/rrwilliams/status/963472189977743371 …
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I think you are right (which is a great reason to work on it!) There are some interesting oddnesses: see for example one of
@michael_nielsen s last papers before leaving quantum https://arxiv.org/abs/quant-ph/0502070 …
You may have meant a later followup, e.g.: https://arxiv.org/abs/quant-ph/0701004 … (Thanks Dave. I regret not developing this much further. Though Lenny Susskind & co have been: https://arxiv.org/abs/1608.02612 )
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I have always had a suspicion that you are still secretly working on this in an attic somewhere. Suspicion. Or a dream. Or a nightmare.
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It certainly seemed - and seems - to me a much more natural problem than classical circuit lower bounds. But that's not to say easy...
End of conversation
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