

Quantum computers no better than classical ones for NP-complete problems. - amichail
http://arstechnica.com/science/news/2010/06/magic-quantum-wand-does-not-vanish-hard-maths.ars#

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michael_nielsen
This has almost certainly only been shown for a restricted class of adiabatic
quantum computers. The full adiabatic quantum computing model is equivalent to
ordinary quantum computing (<http://arxiv.org/abs/quant-ph/0405098> ). If the
linked article is literally correct, then that means quantum computers can
efficiently solve NP-complete problems if and only if classical computers can
efficiently solve NP-complete problems. That may be true, but I'd be very
surprised if someone has proved it.

My guess: the paper under discussion probably shows that some particular
adiabatic approach to solving NP-complete problems fails - most likely, some
variant on the ideas in <http://arxiv.org/abs/quant-ph/0001106>. That's well
and good, but a long way from proving that quantum computers are no better
than classical at solving NP-complete problems. Variants on this result have
been floating around for years - I first heard of one in 2000. This is
probably an improvement on those early results.

Unfortunately, the link to the original paper is broken at present, so that's
just a guess.

~~~
amichail
If such a result were proved, what would happen to the field of quantum
computing?

~~~
michael_nielsen
Hard to say. My first instinct is probably not a whole lot. It's more or less
conventional wisdom in the field that quantum computers are unlikely to be
able to solve NP-complete problems in polynomial time. The argument for this
conventional wisdom is heuristic (and certainly open to doubt, maybe most
people are wrong), and it's in this paper: <http://arxiv.org/abs/quant-
ph/9701001> But in any case, it's one thing for something to be widely
believed, and another thing to have hard evidence. People might respond quite
dramatically to such evidence.

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SlyShy
As disappointing as this result is, I'm glad that Ars seems to do science
reporting with remarkable clarity.

~~~
algolicious
Actually, as an Ars commenter explains, Ars did kind of a bad job explaining
NP. NP is the class of problems with an easily verified proof for existence,
not the class of all exponentially solvable problems as they seem to imply
(EXPTIME). Example: Is a boolean formula satisfiable? Provided an assignment
for its variables, it is easy to check if it is a satisfying assignment.

~~~
kemiller
Explaining NP-complete to even a technically-educated audience is always
tricky. Sometimes a somewhat misleading explanation is still going to get them
closer to the important bits than a precise technical definition would.

I'd probably write: NP-complete refers to a special class of notoriously
difficult problems. A solution to even one of them would lead to a solution to
all of them, a development which could have radical real-world implications.
(Insert good example here.)

~~~
moultano
I've had a lot of success explaining "easy to check a solution, but hard to
come up with one" to people. It really doesn't matter whether people
understand NP-complete and how polynomial reductions work. Just understanding
what's included under NP is enough.

If I were writing this article, I'd explain NP as above, and then say
"research now shows that there are many problems in NP on which quantum
computers will offer no improvement."

~~~
roundsquare
I remember reading an example of "easy to check but hard to come up with"
which is probably good for non-technical audiences. Its something like: You
walk into a party and you want to know if you know anyone. To find out, you
need to look at everyone and check. Alternatively, someone can point to
someone and say "do you know John" and you can check that much faster.

However, I think that reductions are critical to understanding why we care
about NP-complete problems so much. The best example I've been able to give of
a reduction is "reducing" addition to subtraction.

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sanxiyn
I don't believe this. If this were true, it would imply that the decision
version of the integer factorization problem is not NP-complete. That sounds
too good to be true.

~~~
sirclueless
As far as I can tell, D-Wave's adiabatic quantum computer has never
demonstrated polynomial-time factoring either. The result mentioned in ars
technica (DOI link is down, and a scholar search didn't find it) might also
invalidate the use of said computer for this purpose.

------
hawk
quantum computers are not KNOWN to be better than classical ones for NP-
complete problems (although many believe that no form of computation available
in this universe can solve NP-hard problems in polynomial times)

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wake_up_sticky
What a relief! :)

------
Devilboy
This article seems to say the ADAIABATIC quantum computers aren't better than
classical ones. In other words other quantum computers might still be useful
where D-WAVE's adiabatic approach will not?

The adiabatic quantum computer from D-WAVE has been criticized previously for
not being a 'real' quantum computer.

~~~
mturmon
From the article:

"Furthermore, all types of quantum computers have been shown to be
mathematically identical, so if one won't work, none of them will."

This is vague, and does not say if it pertains to only QC's used on problems
in NP, or in general.

As other posters have noted, the subject resists simplification. For more,
see:

[http://en.wikipedia.org/wiki/Quantum_computer#Relation_to_co...](http://en.wikipedia.org/wiki/Quantum_computer#Relation_to_computational_complexity_theory)

<http://qwiki.stanford.edu/wiki/Petting_Zoo#BQP>

~~~
hugh3
Quantum computers work just fine, they just can't solve NP-complete problems
faster than a classical computer.

This is fine, since nobody except D-wave and their somewhat credulous
investors (including folks who should have known better) ever really thought
they would.

