
BQP Not in the Polynomial-Time Hierarchy in Relativized Worlds - EvgeniyZh
https://blog.computationalcomplexity.org/2018/06/bqp-not-in-polynomial-time-hierarchy-in.html
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selimthegrim
This thread by Henry Yuen puts this in context well:
[https://twitter.com/henrytcs/status/1002233325514194944](https://twitter.com/henrytcs/status/1002233325514194944)

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zitterbewegung
So from my casual reading of the Blog post and Paper BQP is now proven to have
sets of problems that aren't efficiently solvable from classical computers?

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thebzax
Unfortunately, not quite. Note from the blog post that "Since P sits in BQP
which sits in PSPACE we can't prove outright any separations for BQP without
separating P from PSPACE". We still haven't proven P isn't equal to PSPACE.

What BQP does efficiently solve, which classical computers do not, is a
particular "Promise Problem" of the form "Input X is either of type A, B, or
C, please classify it as either A or B". The promise is that I won't give you
any inputs of type C, but you don't know how to tell if I break the promise.

Note also that

>> "In particular, it has been shown there exist languages A and B such that
P^A=NP^A and P^B≠NP^B (Baker, Gill, and Solovay 1975). The fact the P = NP
question relativizes both ways is taken as evidence that answering this
question is difficult, because a proof technique that relativizes (i.e.,
unaffected by the addition of an oracle) will not answer the P = NP question.
Most proof techniques relativize."

from
[https://en.wikipedia.org/wiki/Oracle_machine#Complexity_clas...](https://en.wikipedia.org/wiki/Oracle_machine#Complexity_classes_of_oracle_machines)

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zitterbewegung
Yea, Its been awhile since I studied quantum computation. Thanks!

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tonymillion
That title looks like it was written by a markov chain

