

Quantum computing device hints at powerful future - RiderOfGiraffes
http://www.bbc.co.uk/news/science-environment-12811199

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kondro
Yay, probabilistic computing.

You have a 99.5% chance that your PayPal transaction has succeeded. A bit like
using a NoSQL database.

~~~
sukuriant
It's more useful for problems in the NP-Complete set, where you can write an
algorithm that should take a very long time to perform, but takes very little
time to check.

Take the 3-sat problem, for example. It takes a very long time for
conventional algorithms to produce a correct answer; but, given a potential
solution, it takes very little time to check for correctness. It's this area
that quantum computers could shine in. Get a potential answer from the machine
and check its accuracy very quickly. If wrong, try again.

[edit: if I misunderstand quantum computers, forgive me. This is just what I
thought their allure was]

~~~
gjm11
Quantum computers are not known to be able to solve NP-complete problems in
polynomial time. (Assuming for the sake of argument that we can actually build
them.)

There are problems -- factorization, as others have already said, is the
commonest example -- that (1) are not known to be solvable classically in a
reasonable amount of time and (2) are known to be solvable by a quantum
computer in a reasonable amount of time. But they aren't NP-complete problems.

~~~
vmind
Quantum Computers are able to solve problems of complexity BQP in polynomial
time. BQP is suspected to cover all problems in P, some in NP (but not NP-
complete), and some outside of NP but in PSPACE.
(<http://en.wikipedia.org/wiki/BQP>)

~~~
sukuriant
Ah! That clears things up quite a bit. I'm surprised they're not able to work
at the NP-C set. Is it because the probability of a right answer is so small?

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paulnelligan
Does anyone have any info as to how the art of programming might change with
quantum technology ?

~~~
Estragon
That's getting a bit ahead of where they're at. To the best of my knowledge,
the fundamental assumption behind the QC paradigm, the Copenhagen
Interpretation, has never really been tested.[1] It is possible that a device
like this will constitute the definitive test. The question will be whether
such a system can actually perform a calculation across a superposition of
states. In the systems I am aware of where such a calculation has been
claimed, what actually happened was that a large number of atoms were
manipulated simultaneously, and the "superposition" was potentially across the
specific states in those individual atoms.

My own opinion is that the QC scenario is a _reductio ad absurdum_ for the
Copenhagen Interpretation, and that when a true QC calculation is set up, it
will fail. This is actually an optimistic view, because the Copenhagen
Interpretation is a fundamentally pessimistic assumption: that because we
_don't_ know what's behind a certain observed random distribution, we _can't_.
See the following link for more details. (But IAMAP, and I'm not really
keeping up with this area.)

[1] For more on how the Copenhagen Interpretation evolved, and just how little
empirical basis there is for it, see
[http://books.google.com/books?id=tTN4HuUNXjgC&lpg=PP1...](http://books.google.com/books?id=tTN4HuUNXjgC&lpg=PP1&pg=PA328#v=onepage&q&f=false)

~~~
gjm11
Quantum computation does not in any way depend on the Copenhagen
interpretation.

~~~
Estragon
The QC scenario relies on the superposition of states which collapse
probabilistically when the system is observed. It is precisely this
superposition which enables the massive parallelism the QC scenario promises.
This superposition and probabilistic collapse is a central component of the
Copenhagen Interpretation, as I understand it.

~~~
Jach
Superposition isn't part of the Copenhagen interpretation, nor is decoherence.
Copenhagen is the addition to standard QM (which QC is based on) and states
that the other possibilities we don't observe, also stop existing, making
there only be "one true world". But it's not predicted by standard QM which
predicts MWI: <http://arxiv.org/pdf/0905.1283v1>

[http://www.hpl.hp.com/breweb/quiprocone/Protected/Lecture_2....](http://www.hpl.hp.com/breweb/quiprocone/Protected/Lecture_2.htm)

~~~
Estragon
This might be a matter of semantics. When I say "superposition," I mean the
view that all we could possibly know about a system is represented in its wave
function. This implies an _ontological_ superposition of states until the wave
function is collapsed, as is famously embodied in Schroedinger's cat. It is
this ontological superposition of states which the QC scenario depends on for
massive parallelism: If Schroedinger's cat was the input to your QC function,
you would get to run the function with an alive-cat and a dead-cat input at
the same time. Of course, you only get to see the output for the state the
cat's in when the wave function is collapsed, and a key aspect of search
algorithms like Shor's QC factorization scheme is to make sure that all the
other states cancel out. (Shor's algorithm basically tries all possible
divisors of the target number at the same time, through a superposition
scheme.)

But if the probabilistic component of the QM wave function instead merely
represents our degree of ignorance about the entire system, rather than some
such magical superposition, then the QC system is actually only in _one_ of
the many states on which the computation is supposed to be run simultaneously,
and the promised massive parallelism is just a fantasy.

(Yes, I think a hidden-variables explanation is more likely than the
Copenhagen interpretation. Yes, I know about the EPR experiment.)

~~~
gjm11
It sounds to me as if what you don't believe in is not _the Copenhagen
interpretation_ but _quantum mechanics_. The things on which quantum
computation depends, and that you are being skeptical about, are common to all
interpretations of QM. (Which is just as well, because all interpretations
make the same predictions about our observations -- aside perhaps from some
funny "anthropic" things -- and whether quantum computation works or not is,
at least once the necessary engineering has been done, eminently observable.)

~~~
Estragon

      > The things on which quantum computation depends, and
      > that you are being skeptical about, are common to all 
      > interpretations of QM.
    

I disagree: <http://en.wikipedia.org/wiki/Hidden_variable_theory> (The
"Motivation" section is particularly relevant to this discussion.)

This is not the standard QM, but to the best of my knowledge it is consistent
with the results of all the standard QM experiments.

~~~
gjm11
Quantum computation works just fine in Bohmian QM. (The pilot wave contains
all the same structure you get in a conventional wavefunction, including the
"parallel worlds".)

~~~
Estragon
That's exactly my point. Not only does QC work "just fine" in Bohmian QM, it
_critically depends_ on the Bohmian interpretation of the wave function
probabilities to achieve the massive parallelism it promises. To the best of
my knowledge, there is no empirical basis to that interpretation, and there
are effective QM models which don't need it.

~~~
gjm11
Are you perhaps confusing Born with Bohm? There is no possible sense in which
QC critically depends on anything to do with Bohm.

Neither does it depend on very much about exactly what those Born
probabilities mean. All that matters is that, e.g., when one of them is very
close to 1 and the others very close to 0, you will almost always find
yourself observing an outcome corresponding to the nearly-1 probability.
Again: if you disbelieve that -- which is what you'd need to disbelieve to
have a problem with QC here -- then what you are rejecting is not any
particular interpretation, but _quantum mechanics_ itself as a description of
what the universe does.

~~~
Estragon

      > Are you perhaps confusing Born with Bohm?
    

Sorry for my misunderstanding. I thought you were using "Bohmian" to refer to
the standard interpretation. (I'd forgotten about that reference in the
"Motivation" section of the wikipedia article.) I wasn't referring to the
Bohmian interpretation two comments back, I was referring more to the kind of
hidden variable Einstein had in mind. (I realize it would have to be non-
local.)

    
    
      > All that matters is that, e.g., when one of them is 
      > very close to 1 and the others very close to 0
    

That's just begging the question. The "nearly-1 probability" comes from the
assumption that the initial state in the algorithm is a superposition over a
large number of classical states.

    
    
      > what you are rejecting is not any particular
      > interpretation, but quantum mechanics itself as a 
      > description of what the universe does.
    

No, I accept that the probabilities which come out of the QM formalism
accurately describe the frequencies observed in QM systems _in the aggregate
over many observations._ I don't accept that those probabilities tell the
whole story _in one particular instance._

------
exit
this article doesn't get into what kind of future quantum computing will
enable.

can anyone describe a program which cannot be written (efficiently) today,
which might run on quantum computers eventually?

~~~
wlievens
Shor's algorithm is _the_ classic (pun intended) example:
<http://en.wikipedia.org/wiki/Shors_algorithm>

~~~
Jach
I think this is a better writeup: <http://www.scottaaronson.com/blog/?p=208>

