
Official Google Research Blog: Machine Learning with Quantum Algorithms - Anon84
http://googleresearch.blogspot.com/2009/12/machine-learning-with-quantum.html?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+blogspot%2FgJZg+%28Official+Google+Research+Blog%29
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jb55
The more interesting part of the story is that they're collaborating with
D-Wave to try and get these algorithms running on their hardware. Should be
interesting to see what comes out of this, considering the amount of
skepticism that has been surrounding D-Wave.

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sgk284
When I was working at Google in 2007, D-Wave's CEO came by and gave a talk
about their chips. It was interesting and he was immediately interested in
getting Google on board with access to resources that most of the world
doesn't have.

I remember at the time holding one of the first quantum processors in the
world and thinking how this is going to change history. Even though at the
time it only did a single simple task, it was clear that big things were
coming. One thing he mentioned, and I forget the specifics so I can't really
elaborate, but the chips are designed to be crippled in a certain way that
doesn't allow them to implement Shor's algorithm. Apparently this was at the
request of the NSA. I've no idea if that is still the case, but worth keeping
in mind.

~~~
krisneuharth
I had to look it up so hopefully this is helpful to someone else:
<http://en.wikipedia.org/wiki/Shor%27s_algorithm>

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breck
> So on average it will take you 500,000 peeks to find the ball. Now a quantum
> computer can perform such a search looking only into 1000 drawers. This mind
> boggling feat is known as Grover’s algorithm.

This is a very clear explanation of the benefits of quantum computers. But I
don't grasp how this would work yet.

I read the Wikipedia page, and maybe I just have to struggle more with it, but
it would be great if there was a simpler explanation.

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luchak
As Wikipedia says, in a quantum computer, you have a quantum register (a bunch
of entangled qubits) that holds the result of your computation. The contents
of this register can be visualized as a high-dimensional vector of length 1 --
think of this as a line with one endpoint at the origin and the other
restricted to the radius-1 hypersphere around the origin. Each axis of the
space that this sphere lives in corresponds to one classical value of the
register -- in an 8-qubit register, one axis corresponds to 00000000, another
corresponds to 00000001, etc.

The real problem you solve with Grover's algorithm is this: you have a black
box (usually called an "Oracle operator", but I think the term "Oracle" in
this case is misleading) that negates the value of your register along exactly
one axis (i.e., if the coordinate on the 00010111 axis is .2 - .1i, it becomes
-.2+.1i). You want to figure out which of the 2^n axes in the n-qubit register
your black box negates.

Unfortunately, you don't have the luxury of picking the vector that has a
coordinate of 1/sqrt(2^n) in each direction, and observing what the black box
does to that after a single application, since when you observe your quantum
register you always observe a classical state. In contrast, one solution that
would work would be to solve the problem the classical-computing way: march
through each of the 2^n axes until you find the one you're looking for.

Grover's algorithm gives you a better way. What Grover's algorithm does is
repeatedly apply an operation that nudges your register towards the desired
state -- basically applying a small rotation. After some number of iterations,
the vector representing your register should be pointing in almost the same
direction as the vector representing the state you're searching for. Then you
can measure the contents of the register and, with high probability, get the
answer you were searching for. It turns out you only need O(sqrt(2^n)) queries
(rotations), so it's a substantial improvement over the classical case.

I've probably oversimplified a few things, but hopefully this makes things
clearer than they were before.

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ggruschow
This must be how old mainframe programmers felt reading articles about PCs in
the early 70s.

~~~
osipov
Machine learning with quantum computers is so much more than that: quantum
computation is provably more efficient at solving a large class of problems
than classical computation.

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camccann
Unfortunately, there are also large classes of interesting problems which are
intractable even with quantum computation.

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Devilboy
That's a good thing, it means I'll still have a job 10 years from now!

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gluejar
I'm betting that someone will prove a TANSTAAFL theorem for Quantum computing.
In other words, you might be able to factor in polynomial steps, but each step
will take time proportional to the size of your Hilbert space.

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Estragon
I'm betting that the Copenhagen interpretation of the Quantum mechanics
formalism is false. There is no empirical basis for it, and it is a
fundamentally pessimistic view of physics (that we don't know certain things
because we simply can't know them.) I don't think the superpositions in the
quantum mechanical formalism reflect any objective reality, their just a
standard statistical reflection of our ignorance of the system's total state.
But the notion of quantum computation crucially depends on these
superpositions. To me the vast efficiency gains claimed for quantum
computation are actually a _reductio ad adsurdum_ for the Copenhagen
interpretation accordiing objective reality to these superpositions.

That people are apparently attempting serious implementations of quantum
computation is very exciting to me, because it means these ideas are going to
be severely tested soon.

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Herring
Bell's theorem demands that you give up locality or realism. Either is fine;
historically speaking it's just been easier to give up realism. Of course
physicists found a way to keep both (by splitting the _observer_ up), & MWI's
increasing popularity reflects this. In my view it's useless to argue about
interpretations. Last I checked they had the same predictions.

~~~
Estragon

      In my view it's useless to argue about interpretations. Last I checked they had the same predictions.
    

Not true at all. If the superposition in the QM formalism merely represents
our ignorance about the system's state, rather than an objective reality, then
QC loses the massive parallelism which is supposed to make it so much more
efficient than classical computation.

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Herring
Well nobody argues the wave function represents our ignorance about the
system's state. It's certainly not in the Copenhagen interpretation anyway.
The wave function sacrifices realism.

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Estragon
In the Copenhagen interpretation, the wave function represents our ignorance
of what the system's state will _become_ when _observed_ , but it's taken as
an accurate description of the system's _actual state_ prior to observation.
That is the point of the "Schroedinger's cat" paradox: that under the
Copenhagen interpretation, the cat actually is in a superposition of alive and
dead states, until someone looks in the box. Quantum computation crucially
depends on the objective reality of this superposition. It seems likely to me
that the superposition in the formalism actually just represents our ignorance
of the system's state, not the state itself.

~~~
Herring
_> It seems likely to me that the superposition in the formalism actually just
represents our ignorance of the system's state, not the state itself._

Again, nobody argues that. It's possible to experimentally distinguish between
the two situations (Bell's theorem). This is a bit of a strawman.

Besides the wave function is a complex vector. It can't represent ignorance.
You have to take |ψ|2 to get a real value.

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sunkencity
Nice to see that experience with LISP is a desired qualification for the job
as Experimental Physicist at DWave.

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yters
Interesting, I did not realize that usable quantum chips now exist.

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Devilboy
I have a question about D-Wave. I've been trying to follow their progress in
building multi-qubit adiabatic quantum computers for years now, and I see
Google is working with them now too. But this blog entry states that it's hard
to work out if D-Wave's hardware is really a quantum computer. Why is it so
hard? I mean after all these years they still can't tell if it's actually
working?

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gluejar
To some extent, everything is a quantum computer; the problem is entering in
the program and how accurately you can read out the answer. If I understand
correctly, the scientific advance reported is just doing the first part.

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danbmil99
talk about premature optmimization...

