# Physicists take first step towards super-fast search algorithms for quantum computers

##### July 9, 2009

When you toss a coin, you either get heads or tails. By contrast, things are not so definite at the microcosmic level. An atomic 'coin' can display a superposition of heads and tails when it has been thrown. However, this only happens if you do not look at the coin. If you do, it decides in favour of one of the two states. If you leave the decision where a quantum particle should go to a coin like this, you get unusual effects. For the first time, physicists at the University of Bonn have demonstrated these effects in an experiment with caesium. Their research will be published in the next issue of the scientific journal Science.

Let's assume we carried out the following experiment: we put a coin in the hand of a test person. We'll simply call this person Hans. Hans's task is now to toss the coin several times. Whenever the coin turns up 'heads', his task is to take a step to the right. By contrast, if it turns up 'tails', he takes a step to the left. After 10 throws we look where Hans is standing. Probably he won't have moved too far from his initial position, as 'heads' and 'tails' turn up more or less equally often. In order to walk 10 paces to the right, Hans would have to get 10 'heads' successively. And that tends not happen that often.

Now, we assume that Hans is a very patient person. He is so patient that he does this experiment 1000 times successively. After each go, we record his position. When at the end we display this result as a graph, we get a typical bell curve. Hans very often ends up somewhere close to his starting positions after 10 throws. By contrast, we seldom find him far to the left or right.

The experiment is called a 'random walk'. The phenomenon can be found in many areas of modern science, e.g. as Brownian motion. In the world of , there is an analogy with intriguing new properties, the 'quantum walk'. Up to now, this was a more or less a theoretical construct, but physicists at the University of Bonn have now actually carried out this kind of 'quantum walk'.

A single caesium atom held in a kind of tweezers composed of laser beams served as a random walker and coin at the same time. Atoms can adopt different quantum mechanical states, similar to head and tails of a coin facing upwards. Yet at the microcosmic level everything is a little more complicated. This is because quantum particles can exist in a superposition of different states. Basically, in that case 'a bit of heads' and 'a bit of tails' are facing upwards. Physicists also call this superposition.

Using two conveyor belts made of laser beams, the Bonn physicists pulled their caesium atom in two opposite directions, the 'heads' part to the right, the 'tails' part to the left. 'This way we were able to move both states apart by fractions of a thousandth of a millimetre,' Dr. Artur Widera from the Bonn Institute of Applied Physics explains. After that, the scientists 'threw the dice once more' and put each of both components into a superposition of heads and tails again.

After several steps of this 'quantum walk' a caesium atom like this that has been stretched apart is basically everywhere. Only when you measure its position does it 'decide' at which position of the 'catwalk' it wants to turn up. The probability of its position is predominantly determined by a second effect of quantum mechanics. This is due to two parts of the atom being able to reinforce themselves or annihilate themselves. As in the case of light physicists call this interference.

As in the example of Hans the coin thrower, you can now carry out this 'quantum walk' many times. You then also get a curve which reflects the atom's probability of presence. And that is precisely what the physicists from Bonn measured. 'Our curve is clearly different from the results obtained in classical random walks. It does not have its maximum at the centre, but at the edges,' Artur Widera's colleague Michal Karski points out. 'This is exactly what we expect from theoretical considerations and what makes the quantum walk so attractive for applications.' For comparison the scientists destroyed the quantum mechanical after every single 'throw of the coin'. Then the 'quantum walk' becomes a 'random walk', and the caesium atom behaves like Hans. 'And that is exactly the effect we see,' Michal Karski says.

Professor Dieter Meschede's group has been working on the development of so-called quantum computers now for many years. With the 'quantum walk' the team has now achieved a further seminal step on this path. 'With the effect we have demonstrated, entirely new algorithms can be implemented,' Artur Widera explains. Search processes are one example. Today, if you want to trace a single one in a row of zeros, you have to check all the digits individually. The time taken therefore increases linearly with the number of digits. By contrast, using the 'quantum walk' algorithm the random walker can search in many different places simultaneously. The search for the proverbial needle in a haystack would thus be greatly speeded up.

Source: University of Bonn (news : web)

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##### ciantic
not rated yet Jul 09, 2009
Huh? Is the measurement of this quantum walk step done after *each* step, or after several steps?

What does this "For comparison the scientists destroyed the quantum mechanical superposition after every single 'throw of the coin'. Then the 'quantum walk' becomes a 'random walk', and the caesium atom behaves like Hans." mean exactly?

My interpretation was this: "For comparsion the scientists measured the value after each step.", which lead me to think how did they do the `other` walk? If so, then my conclusion for the quantum walk that leads to the "maximum at the edges" is following: "They measure the value after *several* steps."

Is that right?
##### PPihkala
5 / 5 (1) Jul 09, 2009
"They measure the value after *several* steps."

Is that right?

I think that is so. I understand it so that by doing several steps after each other, without looking what the result is, they kind of get the superpositioned atom to spread into two parts, the left going and the right going one. And then the atom only 'decides' when looked where to stand. Now because it was previously ran into two parts that were ran into borders, it's going to be more probable that you will find it standing at the edges, at either one.
##### SmartK8
not rated yet Jul 10, 2009
It's interesting as well as mind boggling. This article seems to implicate that when a dice is thrown, and the results are not measured (which cannot itself be achieved, thus the experiment with a cesium atom), it behaves as a "quantum walk". So the measurement forces it to behave according to the Bell's curve ("random walk"). To clarify PPihkala. I don't think the atom is split into the parts physically. It is just in a probability superposition. Anyway, this article confuses me a bit. I would expect that measured state (after few throws) will be present equally in all the steps from minimum to maximum. Can someone explain, how the quantum probability forces this type of graph (de facto reversed Bell's curve) ?

Update: I got it I guess. It's because of the interference.
##### Birger
not rated yet Jul 10, 2009
Since there are putative quantum algorithms for even the so-called "Fourier transform" -used by computers for pattern recognition- a tiny quantum computer chip would be able to rival the human brain in its ability to identify objects (a task that requires enormous computer power, but which the brain handles through layers of "neural networks" and massively parallel processing).
One obvious application is the interpretation of CCTV images without human operators.

What many have failed to see is the consequences for modern warfare: anything bigger than a bird or small mammal on the battlefield could immediately be detected by small sensors with such quantum computer chips.
A human-operated armoured vechicle or aircraft, would thus immediately be detected once it broke cover. Small, remotely operated vehicles might survive on a battlefield, but holding captured ground requires a human presence.
In principle, it could make offensive warfare very costly, like WWI before the advent of the tank.
##### ciantic
not rated yet Jul 10, 2009
I found other resources that confirm this for instance in this http://arxiv.org/.../0303081 at the page 4: "If we continued the quantum walk with such a measurement at each iteration we obtain the plain classical random walk on the line (or on the circle)."

and also at the same page: "In the quantum random walk we will of course not measure the coin register during intermediate iterations, but rather keep the quantum correlations between different positions and let them interfere in subsequent steps." thus there exists coin (Hadamarad coin) that when:

throw, look; throw, look; ... 100 times you get bell's curve, but if you do:

throw, throw, look; throw, throw, look; ... 100 times you get curve like in the paper above.

Pretty neat, not sure what the implications are yet.
##### El_Nose
not rated yet Jul 10, 2009
-- Hey remember the advent of classical computing that u learn in sophomore year in college and the class is really boring but you go through the generations on computers real quick so that you at least now how we got to where we are.

This reminds me of the first and second generation of computing where computations were in essence done mechanically like moving this atom around and measuring. I wonder knowing that we will eventually abstract this foundation away can we begin trying to think on that new level of abstration today.

Do we know enough about this layer of abstration to let it go and work a layer higher or are we in need of the engineering invention equivalent of the transistor tube to move away from gears and pulleys again??? PLEASE RESPOND
##### lysdexia
not rated yet Jul 16, 2009
There's no "a dice".

It's easy; the inverse probability plot is for the potential, and the obverse for the cinetic.

Fast is not a speed; glue is fast.
##### ben6993
not rated yet Jul 16, 2009
Thank you ciantic for the reference to Kempe's article. I have downloaded it and skimmed the first half. I can see it is a truly wonderful new area without understanding the non-classical parts yet. It will provide months of bedside reading/learning matter!

Classical random walks seem to behave like the boring stay at home who never ventures far from home. I am not clear whether the quantum random walk particles are like the Ben Fogle adventurer always at either the North or South Pole, ie, stiving to infinity to leave all else behind, or are they exhibiting fractal-like behaviour where they stay within bounds and have a complex pattern of location?

Pauli's exclusion principle, I think, pertains to different electons not being in the same state. And the electons near an atom have shell patterns of locations. But the particle in this random walk is on its own. Well not completely on its own as it is operating within the laws of physics, and therefore sits in spacetime. And the single particle appears to be able to be everywhere at the same time, with varying probablilities. So is the single particle interacting with itself? And so can the exclusion principle apply to the varying possible positions of the single particle? And will a single particle interact with itself to locate in shells even where there is no central nucleus?

What would a quantum random walk be like for two particle in an enclosed space?

A complex, and beautiful, fractal picture like a mandlebrot diagram can result from applying a simple formula. Would a particle, or point, generating the 2-D mandlebrot picture, using the simple formula for its position, appear to be located in shells if it were only measured in 1-D? Likewise is the quantum random walk particle inabiting higher dimensions where it has a rich pattern that defaults to shells when looked at in reduced numbers of dimensions?

And can you take a mandlebrot picture and re-run it but this time taking the point or particle on a quantum random walk as it also follows the simple formula? Ie make it follow the formula but with an extra random element included in the formula?