Quantum Lower Bounds by Polynomials · HackerPapers discussions

Quantum Lower Bounds by Polynomials — mentioned by j2kun

Thu, 18 Jun 2015 18:08:24 GMT

Yes. They refuted two conjectures 1. From 1998 [1] that the biggest gap in this model between quantum and classical was quadratic. (they got quartic) 2. From 1984 [2] that the biggest randomized/classical gap was something like N^0.75 (they got quadratic) The reason I call these "major" is perhaps not exciting to people outside of academia: smart people tried to do better than [1] and [2] but couldn't for > 10 years. These works definitely deepen our theoretical understanding of the differences between quantum/randomized/classical computing. But you have to take it with the grain of salt that…

Paper and discussion history. A mention is not an endorsement.

Quantum Lower Bounds by Polynomials — mentioned by michael_nielsen

Thu, 19 Jun 2014 23:27:32 GMT

That's right. The search result, however, assumes the only way of accessing the database is through a black box oracle. That's why I wrote "non-oracle" in my previous comment. It's called an oracle because the internals of the black box are assumed to be unknown. That assumption is necessary in order to prove that classical computers need ~ N operations. If you know something about the internals of the oracle, then it may well be possible to exploit what you know to search faster. The quantum search algorithm is very interesting. However, most people in the field would, I think, agree that a…

Paper and discussion history. A mention is not an endorsement.