Thursday, February 23, 2006

Suitably Advanced Technology...

"A non-running computer produces fewer errors."

One of the more interesting cognitive obstacles to quantum computing is the idea of superposition - that is, like Schrodinger's cat being alive and dead at the same time, the computer can be on and off at once. The waveform may collapse - the program may finish - and at the end you may find out the program never ran in the first place. Here is a little thought-experiment to help guide the perplexed.


Blogger Mister Spark said...

Quantum computer works best switched off

* 22 February 2006
* From New Scientist Print Edition

Even for the crazy world of quantum mechanics, this one is twisted. A quantum computer program has produced an answer without actually running.

The idea behind the feat, first proposed in 1998, is to put a quantum computer into a “superposition”, a state in which it is both running and not running. It is as if you asked Schrödinger's cat to hit "Run".

With the right set-up, the theory suggested, the computer would sometimes get an answer out of the computer even though the program did not run. And now researchers from the University of Illinois at Urbana-Champaign have improved on the original design and built a non-running quantum computer that really works.

They send a photon into a system of mirrors and other optical devices, which included a set of components that run a simple database search by changing the properties of the photon.

The new design includes a quantum trick called the Zeno effect. Repeated measurements stop the photon from entering the actual program, but allow its quantum nature to flirt with the program's components - so it can become gradually altered even though it never actually passes through.

"It is very bizarre that you know your computer has not run but you also know what the answer is," says team member Onur Hosten.

This scheme could have an advantage over straightforward quantum computing. "A non-running computer produces fewer errors," says Hosten. That sentiment should have technophobes nodding enthusiastically.

Journal reference: Nature (vol 439, p 949)

11:19 PM  
Blogger Mister Spark said...

Elitzur-Vaidman bomb-testing problem
From Wikipedia, the free encyclopedia
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In physics, the Elitzur-Vaidman bomb-testing problem is a thought-experiment in quantum mechanics, first proposed by Avshalom Elitzur and Lev Vaidman in 1993. It employs quantum superposition in order to construct a mechanism for ascertaining whether a measurement has taken place.

The bomb-testing problem is illustrated by use of the following analogy: Consider a collection of bombs from some dubious source, so that it is not certain which, and indeed how many, of the bombs are dud. Say we need to know which are usable bombs. Clearly we can accumulate dud bombs by throwing the bombs, one by one, at a wall, and collecting the ones that do not explode. Unfortunately this process does not work in reverse; the only way of finding out which bombs are usable destroys them. Just to make the problem a little harder we will specify that the trigger of each bomb is sensitive to a single photon. Specifically, the bombs either absorb the photon and explode, or transmit the photon and are duds. It is, in principle, impossible to identify usable bombs by any nondestructive classical process. However, through a mode of observation known as counterfactual measurement which relies on quantum mechanics, we can solve this problem.

We set up the following experiment: A single photon is emitted from a light source (A) and reaches a half-silvered plane mirror, meaning the photon either passes through or is reflected, with an equal chance at either. Under quantum mechanics, the interference effects of all possible paths taken are still noticed by photons, even though only one path is physically taken. Thus, we have quantum superposition whereby the photon has both passed through the half-silvered mirror and been reflected at an angle, but we still have only one photon. On one path, the photon would encounter a bomb (B). If the bomb is working, then the photon gets absorbed, else the photon will pass through the dud bomb unaffected. With fully silvered plane mirrors, the two paths are reflected so they collide at a second half-silvered plane mirror such that the two lengths travelled are equal. Then, interferometers (C) and (D) measure which way the photon exits this system. For ease of explanation, assume (A) emits the photon horizontally, and the (A)->(B) segment is considered the unreflected, lower route.

* if the bomb is a dud
o the photon both (i) passes through the 1st half-silvered mirror and (ii) is reflected
o because the bomb is a dud, the photon travelling in the lower route is not absorbed
o whichever path the photon actually took is irrevelent since the effect of its alternate route destructively interfer with it at the 2nd half-silvered mirror
o since the input photon is horizontal, then upon interference, the exiting photon must leave the device horizontally
o thus, the interferometer at (D) notices the photon, and the one at (C) does not.
* else
o logically, the bomb is real
o the photon both (i) passes through the 1st half-silvered mirror and (ii) is reflected
o if the photon really took the lower route
+ because the bomb is real, this photon triggers the bomb and it explodes
o else
+ logically, the photon really took the upper route
+ the effects of the photon taking the lower route are not noticed because it's not possible for a photon on the lower route to pass through a real bomb without being absorbed, hence the lower route photon could not possibly continue to interfer with the one travelling on the upper route
+ the photon on the upper-route now both (i) passes through the 2nd half-silvered mirror and (ii) is reflected
+ if the photon really was reflected
# The interfermoter at (C) notices, the one at (D) does not.
+ else
# logically, the photon passed through
# The interfermoter at (D) notices, the one at (C) does not.

Therefore, with the above theoretical behavior, we can conclude which If-branch/branches was/were taken, ultimately revealing whether the bomb was real or not, based on the observed effects which must be one of the following:

1. The bomb exploded. Obviously it was real.
2. The bomb does not explode. Only (C) received anything. Logically, the bomb must be real.
3. The bomb does not explode. Only (D) received anything. No information was learned. Either the bomb is a dud, or it is real.

We run the experiment many times if the ambiguous 3rd observation is made. Sometimes good bombs explode, but at other times we are guaranteed of finding a good bomb without wasting it.

In 1994, Zeilinger actually performed an equivalent of the above experiment. In 1996, Kwiat et al have devised a method, using a sequence of polarising devices, that efficiently increases the yield rate to a level arbitrarily close to one.

11:19 PM  

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