22. Apr 2008
An artcile in the new Nature (probably behind the paywall) called “Quantum computation: The dreamweaver’s abacus” discusses first successful experiments that for the first time proved the existence of quasi-particles of quarter charge that have the properties needed to build qubits for quantum computing. Wait? Quasi-particles? Qubits? What?
Well, I can’t even start telling about quantum computing, that is because I don’t have much of a clue about it, only small hints that I should shed some light on eventually. But I investigated the other part. Quasiparticles are an interesting concept of physics, with the most prominent appearance in solid-state physics where you describe the movement of the atoms as quasi-particles (called phonons, imagine a sound wave running through a medium as a line of balls connected by springs. The state of exciation, or the mode as it is called, is seen as if it were a particle. You can just calculate an electron and a phonon hitting each other!). Now, the interesting concept used here is about quasi-particles in two dimensions.
Our world is three-dimensional (at least), so why are we even talking about two dimensions outside if a theorist’s mind set? Well, just imagine a very fine layer of metal - and you know that technology is able to produce these - then electrons moving through this layer will have no choice but to visit a two-dimensional world.
Now, what’s with the quarter charge? Isn’t the nice thing about elementary charges that they are, well, undividable? As long as we are talking free particle, this is true. A quark carries a third of an elementary charge, but it is confined in, let’s say, a proton, and that one carries one elementary charge (called e). Now we are in the quasi-particle regime, so it’s not actually little balls flying around we’re discussing. In the quantum world, one of the most important concepts is that everything comes in steps - in quantums. Energy is quantized, that’s about the first thing you learn in Quantum Mechanics. You know that electrons can exist in discrete orbits around the core of the atom. Why? Quantized energy and momentum. If we take a our-world phenomenon and move to a quantum scale, you are bound to find quantified stuff - like with the Hall effect. Take a metal plate, send current through the plate, apply a magnetic field perpendicular to the plate, you will move the electrons and create a voltage and thus an electric field directed perpendicular to current flow and magnetic field. By measuring the effect of this electric field described by the Hall resistance, you can determine the strength of the magnetic field. Now move to the microscale, to the two-dimensional system described above, and so will have the Quantum Hall effect - the Hall resistance will move only in steps (at low temperature). Again, it is because energy is quantized. Electrons in one energy state cannot continously move between states but have to get enough energy in one collision to jump to another level - like excitation in an atom. At low temperature, this rarely occurs, so you can see the steps in resistance.
Now comes the crazy part, and I’m also rather lost here now. But normally, energy levels are so that higher states are a multiple of a ground state energy, integer multiples for the atom. This is true here, and called the integer Quantum Hall effect. But there’s also a fractional Quantum Hall effect, having the property of small fractions like 1/3 or 3/5 - and there the theorists come running, introduce a concept of quasi-particles, and assign fractional charges to them. Bear with me - I can’t really explain this correctly yet as I’m trying to grasp the concept myself.
So, let’s hurry over this and just accept that there are quasi-particles of fractional charge in these events. Now what’s new? First of all, these particles, called anyons, are neither fermion nor boson. Normally, if you have two identical particles and let them swap place, this will not change anything. Fermions will multiply their wave function by -1, but you take the square of the wave function for observation anyways…now these new anyon things, and mind you they can only occur in two dimensions, our 3D-world only allows fermions and bosons, the way the anyons are swapped matters. The way their wave function will change is different! What does this mean for computing? If they have the additional trait that, if you do several swaps and the order matters (it usually doesn’t, that’s Abelian behavior), you can use that for computing…
Now, you need quarter-charged quasi-particles, and these have been experimentally discovered for the first time.
For a much more thourough discussion of anyons, see this post by someone who actually knows what he’s talking about.
