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Lance Fortnow

@fortnow

Computational Complexity Theorist
Chicago lance.fortnow.com Joined July 2008
390 Following 7K Followers 6.4K Posts

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Lance Fortnow @fortnow
We've known since the 90s that there is no exponential quantum advantage for solving non-structured black-box problems. The resolution of the Aaronson–Ambainis conjecture tells us the same result holds even if the algorithms only need to get most inputs correct.
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Lance Fortnow @fortnow
In 1998, John Rogers and I asked whether P = BQP relative to a random oracle (under an assumption like P=PSPACE unrelativized). This new result proving the Aaronson-Ambainis conjecture gets close, implying (BQP in Average-P)^R.

psi.inc/research/aaron…
psi.inc A proof of the Aaronson-Ambainis conjecture A proof of the Aaronson-Ambainis conjecture about quantum speedups on random inputs, with a complete formalization in Lean.
0 replies 9 reposts 45 likes 3.2K views View on X
Lance Fortnow @fortnow
Cryptographic assumptions are not that we don't have an efficient algorithm for, say, breaking RSA, but there is no efficient algorithm. The distinction is important because no matter how powerful AI gets, it can't find what isn't there.