Re: About Quantum Computing

[charleskmhui@yahoo.com]

Does any erudite person here entertain me about how to use Anyons to
do quantum computing? I read the Frank Wilczek's interview on the Edge
web-site:
http://www.edge.org/3rd_culture/wilczek09/wilczek09_index.html

Does the collective bosonic behavior of electrons at low temperature
is theoretically predicted by his QCD theory or just experimentally
achieved a technically smaller scale of what called Bose-Einstein
condensate but with electrons instead of liquid Helium?

Any other Fermionic material demonstrates collective bosonic behavior?

Any other theoretical guy has played with idea like Bosonic matter
near blackhole hehaves collectively as Fermionic matter?
When I was young I had fantasized that the Universe would be very dull
if everything can be classified as "black or white". This kind of
large scale collective behavior sounds more intriguing to me. Thanks.

Charles Hui

[Igor Khavkine]

On Jan 22, 2:40 am, charleskm...@yahoo.com wrote:
> Does any erudite person here entertain me about how to use Anyons to
> do quantum computing? I read the Frank Wilczek's interview on the Edge
> web-site:http://www.edge.org/3rd_culture/wilczek09/wilczek09_index.html

Don't know anything about it myself, but Google spits out what seem
like useful references:

http://en.wikipedia.org/wiki/Topological_quantum_computer
http://online.kitp.ucsb.edu/online/exotic_c04/preskill/

> Does the collective bosonic behavior of electrons at low temperature
> is theoretically predicted by his QCD theory or just experimentally
> achieved a technically smaller scale of what called Bose-Einstein
> condensate but with electrons instead of liquid Helium?

Umm, the article doesn't speak of bosonic behavior at low
temperatures, only anyonic behavior. But as it happens,
superconductivity is example of bosonic behavior in an electron system
at low temperatures (electrons bind into Cooper pairs and behave like
bosons). Neither has anything to do with QCD.

> Any other Fermionic material demonstrates collective bosonic behavior?

Another well known example is the so-called Luttinger fluid. If you
put electrons in a very thin wire where quantum effects become
important (a quantum wire), then the electrons start collectively
acting as a bosonic system. There are probably other

> Any other theoretical guy has played with idea like Bosonic matter
> near blackhole hehaves collectively as Fermionic matter?

While the transformation from fermions to bosons used to solve the
Luttinger fluid model (bosonization) is in principle reversible
(turning bosons into fermions is sometimes called fermionization), I
don't know of any physical examples where it is applicable. But that
doesn't mean that one doesn't exist.

Also, involving black holes in the mix would be surprising to me. As
far as we know, nothing special happens to matter near a black hole
(excluding vacuum effects), except that the gas that spirals in heat
up. Unless constituent particles start falling apart, matter at hot
temperatures usually behaves in a simpler rather than a more
complicated way. So chances for any fermionization in that context are
slim.

Hope this helps.

Igor

[xepma]

I didn't read the article from Wilczek (might do that later), but I can tell you this.

Quantum Computing by means of anyons has become quite a growing research area over the past few years. It is usually refered to as Topological Quantum Computation, where the "topological" refers to the fact that one makes use of so-called topological degrees of freedom. These degrees of freedom are of a non-local nature (at least the one that I am familiar with), which is what makes them so appealing for use of quantum computation. Disturbances coming from heat, photons, phonons and so on are all caused by local interactions, meaning that topological degrees of freedom are unaffected by them. This causes a quantum computer based on topological degrees of freedom to be unaffected by any type of decoherence - which is precisely the plague that haunts "convential" quantum computers.

One promosing way of realising these topological degrees of freedom is through means of non-Abelian anyons. These are particles which possess a generalized form of statistics, much richer than conventional fermions or bosons. It is well known (and actually put forth by Wilczek) that such forms of statistics are caused by topological terms in the action. An important note is that these systems are only realized in (2+1) dimensions.

Examples of realizations of non-Abelian anyons have been proposed, although no conclusive evidence has been put forth (yet). Most arguments are on the basis of numerics or indirect experiments (such as measuring the charge of the particles). Where can you find them? First off, there are some lattice models out there, Kiteav's honeycomb model is by far the most famous one. Some people try to build such lattice models directly using arrays of josephson junction, but don't ask me what's the progress on that.

However, what initially sparked this whole area is the famous fractional quantum Hall effect. It's quite likely that the excitations found in these (2+1) dimensional systems are indeed of an anyonic nature. The big question right now is wether they are of a non-Abelian nature (meaning these excitations follow non-Abelian statistics), and, if so, if they are suitable for Topological Quantum Computing.

I have much more to tell about this subject - I haven't even gotten to the actual computing stuff. Let me know if you are interested in more.

I recommend the following article:

Non-Abelian Anyons and Topological Quantum Computation
http://arxiv.org/abs/0707.1889