Home-made lattice calculation? The topic of Lattice QCD or Lattice gauge theory or even Lattice field theory is quite old now. And the main reason for the interest in the topic is the ability to calculate nonperturbative stuff on a computer. 
It seems that to do research with lattice you need an access to some supercomputer. But now everyone can afford something that is as powerful as supercomputers 20 years ago. Maybe it possible to redo some of the results of that time? 
Is there any project that is:


*

*Relatively simple.

*Allows to calculate some real-world quantity (like mass of the proton).

*Can be done with an average home computer.

 A: You may try to download QCD software for CUDA - using GPU etc. - at

http://nemea.ist.utl.pt/~ptqcd/

See also

http://www.google.cz/search?q=cuda+qcd

But I don't have any experience and I don't expect the work to be a user-friendly smooth sailing. ;-)
A: If you don't have much experience with Monte Carlo simulations, you might want to start with simulations of the 2d Ising model, which is a lot less complex than SU(N) Yang-Mills or QCD.  Monte Carlo simulation is mostly an art, since we don't usually have rigorous error bounds.  You'll learn the art faster if you can reduce the time your simulations take, and 2d Ising model sims are extremely fast.  You can do them in Python on a modern laptop in a matter of minutes.  
Try tuning the hopping parameter until you see the phase change.  See if you can extract critical exponents and check them against the exact solutions.
A: You could check out pyQCD here: http://www.github.com/mspraggs/pyQCD. It's feature set is not huge and it's still not mature but it can do the basic lattice calculations using quenched configs: propagator calculation and Wilson loops etc.
If you want to get involved with the project you're very welcome (though given you asked two years ago you may no longer be interested).
A: While not strictly lattice QCD, Michael Creutz' 30 year old lattice gauge papers have very simple C implementations (!).
For example, look at this paper, which gives a very readable explanation of lattice gauge simulations, with source code:
http://latticeguy.net/mypubs/pub165.pdf
The source code is also available here:
http://thy.phy.bnl.gov/~creutz/z2/
This compiles and runs out of the box and reproduces the results in the paper. Current papers like the portugese GPU groups' mentioned by Lubos all build on Creutz's 30 year old stuff.
A: You don't need a really big computer. 
Peter LePage used to do talks where he'd ask the audience fro a "random" number as the beginning of the talk (but not 7, 17, 42, or 69 'cause he'd already done those) and start a simulation on one screen with that number as a seed. Then he'd give a talk on how to speed up LQCD calculations on the other screen while his PII 200 MHz laptop crunched a $b\bar{b}$ state during the talk.
But lets talk about that.
First, heavy flavor is easier to do than anything involving light quarks. Especially $u$ or $d$ quarks. You certainly want to learn this business with a faster problem than the proton mass.
Second, "relatively simple" in LQCD is still pretty complicated. Peter's 45 minute talk was intended to give people who knew roughly what a naive LQCD calculation looked like an idea of how his very clever trick for optimizing the business worked. I also sat through four hours of the same thing at a graduate summer school where he was teaching the technique and I only sort of got it (because it was targeted at students who were doing LQCD).
This is a big project.
