
A Problem That Only Quantum Computers Will Ever Be Able to Solve - jonbaer
https://www.quantamagazine.org/finally-a-problem-that-only-quantum-computers-will-ever-be-able-to-solve-20180621/?href=
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fyi1183
This is basically the TCS version of a clickbait headline. It's a separation
of BQP and PH by an oracle. Certainly a nice result, but to put it into
context, we also have a separation of P and NP by an oracle. Yet, we are very
far away from _actually_ proving that P and NP are distinct.

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evanpw
Any time I hear something sensational about quantum computing, I check Scott
Aaronson's blog for the real story. Here's his blog post on this topic:
[https://www.scottaaronson.com/blog/?p=3827](https://www.scottaaronson.com/blog/?p=3827).

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qop
That webpage is the hardest thing to read on a phone screen. Dark grey on
black, why would he ever think that's a good choice??

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dwighttk
I think the white box behind the text must not have loaded on your phone.
Looks fine to me.

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mroll
This article makes it seem like the problem that separates BQP and PH is one
the classical computers literally cannot solve, given any amount of time. I
don't believe that is actually what's going on. If it were the case, this
result would have falsified the Church Turing Thesis, and there would be a lot
more hype around this.

Please correct me if I'm wrong.

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skate22
P != quickly solvable by a classical computer.

P means solvable in polynomial time relative to the size of the problem, which
could still take longer than the universe has existed

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doubleunplussed
Given that computer scientists use the word "efficiently" to mean "in
polynomial time", I'm not too upset at using "quickly" to mean the same.

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skate22
Idk, I majored in CS and I don't use the term efficient or quick to imply
relative asymptotic time complexity.

Consider for example a randomized quicksort (O(n^2) worst case) is often
faster than say mergesort (O(nlog(n)) worst case)) for small lists due to
reduced overhead. I know these are both polynomial, but relatively speaking,
randomized quicksort can be more efficient & quick.

In the real world we can make certain assumptions about our problem domain,
where the most 'efficient' solution for your business problem may not have the
smallest asymptotic time complexity.

Maybe it's fair to assume everyone reading this article knows what the auther
means & i'm just being that guy, but I still don't like ambiguity lol

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doubleunplussed
It's used when talking about the extended Church-Turing thesis [1]:

> "A probabilistic Turing machine can efficiently simulate any realistic model
> of computation." The word 'efficiently' here means up to polynomial-time
> reductions.

Real-world efficiency doesn't necessarily factor into what theoretical
computer scientists are interested in.

[1]
[https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis](https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis)

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ikeboy
>The actual best way to distinguish between complexity classes like BQP and PH
is to measure the computational time required to solve a problem in each. But
computer scientists “don’t have a very sophisticated understanding of, or
ability to measure, actual computation time,” said Henry Yuen, a computer
scientist at the University of Toronto.

>So instead, computer scientists measure something else that they hope will
provide insight into the computation times they can’t measure: They work out
the number of times a computer needs to consult an “oracle” in order to come
back with an answer. An oracle is like a hint-giver. You don’t know how it
comes up with its hints, but you do know they’re reliable.

This is not how it works, at all.

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RobotCaleb
Oh?

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ikeboy
1\. You don't measure the number of steps, you prove that it's bounded by some
function of input length.

2\. You don't work off number of oracle calls, but number of total steps with
an oracle call counting as one step.

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RobotCaleb
Thanks for expounding.

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supermdguy
Can't quantum computers be simulated on classical computers? Doesn't that mean
that any problem solvable by a quantum computer can be solved by a classical
computer, given enough resources? If so, isn't the headline that "Only Quantum
Computers Will Ever Be Able to Solve" misleading?

I don't know much about this subject, so I'm assuming one of my assumptions is
wrong.

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jacobolus
> Can't quantum computers be simulated on classical computers?

The simulation gets exponentially slow, to the point that the fastest
classical computers we have are not practical for simulating even modestly
sized quantum systems.

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zakk
Regarding (a), the approximation can be made as good as you want. However you
are right on (b) it gets exponentially slow.

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transmissible

      Imagine you have two random number generators, each 
      producing a sequence of digits. The question for your 
      computer is this: Are the two sequences completely 
      independent from each other, or are they related in a 
      hidden way?
    

That, right there, should tell absolutely everyone, by intuition alone, that,
despite assurances from industry experts that flaws leading to breaks (
_plain-text discovery faster than brute force_ ) are universally impractical,
even with all the energy of a dyson sphere, that there are classified
equations for back doors baked into all modern, commercially used
civilian/consumer-grade cryptographic algorithms.

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rblatz
I'm not 100% sure which side you are taking, but I think you are saying all
common crypto is backdoored. That seems like a giant logical leap with
absolutely no hints as to why you landed at that conclusion based on your
quote.

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davesque
How to efficiently simulate a quantum circuit? _Badum ching_

I'll be here every night, ladies and gents.

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taejo
If you can prove that simulating a quantum circuit cannot be done in P, that's
a breakthrough you should publish. I'm 80% sure that even if you prove it's
not in PH, you'll be the first.

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Lind5
Quantum computing is coming. How quickly isn’t clear, although the first
versions of this technology are expected to begin showing up over the next few
years, with the rollout across more markets and applications expected by the
middle of the next decade. [https://semiengineering.com/quantum-computing-
becoming-real/](https://semiengineering.com/quantum-computing-becoming-real/)

