Sometimes you slog through tons of papers and wonder how much the whole huge mess really matters. But then there are days like today where I found two papers which I think completely and totally rock. Maybe they don’t really matter, but they are really interesting. The first paper appear on the arXiv today, so I really didn’t have to dig for it, but the other paper I just stumbled upon and somehow missed it when it came out in 2002.
Paper 1: quant-ph/0401137
“Fast simulation of a quantum phase transition in an ion-trap realisable unitary map” by J.P. Barjaktarevic, G.J. Milburn, Ross H. McKenzie. The idea in this paper is very beatiful. Consider a system with a Hamiltonian which posses a quantum phase transition. On a quantum computer it is possible to simulate the dynamics of this Hamiltonian. Suppose that your Hamiltonian is a sum of two noncomuting terms H_1 and H_2 and that you can easily implement evolution according to each of these terms separately, i.e. you can do exp(iH_1t) and exp(iH_2t). One way to then simulate the full Hamiltonian is to “trotterize” the evolution and perform alternating infinitesimal exp(iH_1 dt) exp(iH_2dt) exp(iH_1 dt) exp(iH_2 dt)… =exp(i(H_1+H_2)t)+small error. But suppose that you don’t do this (because, for example you can’t really do good infinitesimal evolutions in the real world!) So instead you use “big” steps exp(iH_1T)exp(iH_2T)… Now you can ask, does this system have a quantum phase tranisition! So in what sense does the “big” evolution model have the same properties as the “infinitesimal” evolution mode? In this paper the authors address this issue for the ising model with a transverse field. And indeed, the authors present strong evidence that there is a quantum phase transition in the behavior of this “big” model! A summer student and I worked a bit on this problem for a different decomposition of the same Hamiltonian. As a nice summer project the summer student, Jaime Valle, wrote code to simulate this evolution. In this model we indeed did see evidence of the phase transition. And now we see that for the decomposition choosen by these authors there is direct analytic evidence of the quantum phase transition!
The second paper that I discovered which I loved was quant-ph/0206016, “The Dirac Equation in Classical Statistical Mechanics” by G.N. Ord. Now this paper, and a series of other papers by this author and coworkers, rocks! What they show is that there is a microscopic statistical mechanical model for the Dirac equation in one dimension! There is a famous prescription for obtainin the Dirac equation in one dimension which is due to Feynman. Basically this prescription works as follows. Consider a particle which moves either forwards or backwards at the speed of light. If you want to calculate the amplitude for the particle to go from spacetime point A to spacetime point B, you simply take all paths for such a particle and associate with it an amplitude which is (im)^(# corners) where m is an infinitesimal parameter, i is the square root of minus 1 and the # corners it the number of times the particle switches directions in the path. If you use this to calculate the amplitudes for all of the paths between A and B and add up all of these amplitudes, you get the kernel for the Dirac equation in one dimension!
What Ord talks about is similar to Feynman’s prescription but what Ord shows how it is possible to construct a model where the statistics of the dirac equation fully explained by a microscopic classical model. One of his version of this model has some very nice properties, like being a beautiful nonlocal hidden variable model of the Dirac equation (it is interested that even for one particle, one gets a nonlocal hidden variable model)
Childhood's End
Who are you and who am I
To say we know the reason why?
Some are born; some men die
Beneath one infinite sky.
There’ll be war, there’ll be peace.
But everything one day will cease.
All the iron turned to rust;
All the proud men turned to dust.
And so all things, time will mend.
-Pink Floyd, Childhood’s End
What Would Teller Do?
Only time will tell if and when the problems of building a quantum computer can be overcome .As information becomes the worlds most valuable commodity, the economic, political and military fate of nations will depend on the strength of ciphers. Consequently, the development of a fully operational quantum computer would imperil our personal privacy, destroy electronic commerce and demolish the concept of national security. A quantum computer would jeopardise the stability of the world. Whichever country gets there first will have the ability to monitor the communications of its citizens, read the minds of its commercial rivals and eavesdrop on the plans of its enemies. Although it is still in its infancy, quantum computing presents a potential threat to the individual, to international business and to global security. -Simon Singh
Church Time
Perhaps it is time for me to get religion.
Quantum Computing Schools
Here is a list of school rankings of graduate physics and computer science departments. These schools should all be doing quantum computing, No?
| phys | cs | phsy+cs | |
| Massachusetts Institute of Technology |
5 | 4.9 | 9.9 |
| Stanford University (CA) | 4.9 | 4.9 | 9.8 |
| University of California�Berkeley� |
4.9 | 4.9 | 9.8 |
| Princeton University (NJ) |
4.9 | 4.3 | 9.2 |
| California Institute of Technology |
5 | 4.1 | 9.1 |
| Cornell University (NY) | 4.6 | 4.5 | 9.1 |
| University of Illinois�Urbana-Champaign |
4.5 | 4.6 | 9.1 |
| Harvard University (MA) | 4.9 | 3.7 | 8.6 |
| University of Texas�Austin |
4.1 | 4.4 | 8.5 |
| University of Washington | 4 | 4.4 | 8.4 |
| Carnegie Mellon University (PA) |
3.5 | 4.9 | 8.4 |
| University of Maryland�College Park |
4.1 | 4 | 8.1 |
| University of Wisconsin�Madison |
4 | 4.1 | 8.1 |
| Columbia University (NY) | 4.3 | 3.7 | 8 |
| University of Michigan�Ann Arbor� |
4.1 | 3.9 | 8 |
| University of California�Los Angeles |
4 | 3.9 | 7.9 |
| Yale University (CT) | 4.2 | 3.6 | 7.8 |
| University of Chicago | 4.6 | 3.2 | 7.8 |
| University of California�San Diego |
4 | 3.7 | 7.7 |
| University of Pennsylvania |
3.9 | 3.8 | 7.7 |
| Brown University (RI) | 3.5 | 3.9 | 7.4 |
| Georgia Institute of Technology |
3.4 | 4 | 7.4 |
| University of California�Santa Barbara |
4.3 | 2.9 | 7.2 |
| Johns Hopkins University (MD) |
3.9 | 3.3 | 7.2 |
| Rice University (TX) | 3.4 | 3.8 | 7.2 |
| University of Colorado�Boulder |
3.9 | 3.2 | 7.1 |
| SUNY�Stony Brook | 3.8 | 3.3 | 7.1 |
| Duke University (NC) | 3.4 | 3.7 | 7.1 |
| Purdue University�West Lafayette (IN) |
3.4 | 3.7 | 7.1 |
| University of North Carolina�Chapel Hill |
3.3 | 3.8 | 7.1 |
| Rutgers State University�New Brunswick (NJ) |
3.7 | 3.3 | 7 |
| Ohio State University | 3.7 | 3.2 | 6.9 |
| University of Minnesota�Twin Cities |
3.7 | 3.2 | 6.9 |
| Penn State University�University Park |
3.6 | 3.2 | 6.8 |
| University of Virginia | 3.3 | 3.5 | 6.8 |
| Northwestern University (IL) |
3.5 | 3.1 | 6.6 |
| University of California�Irvine |
3.3 | 3.3 | 6.6 |
| University of Southern California |
3.1 | 3.5 | 6.6 |
| University of Massachusetts�Amherst |
3 | 3.6 | 6.6 |
My Dad
For those interested, I’ve pasted the article from the local newspaper, the Siskiyou Daily News about my dad.
Continue reading “My Dad”
Those Silly Pranksters
From Foxtrot:
TV: Welcome to the BCS national championship football game, here at the Louisiana Superdome.
TV: Let’s begin by acknowledging that there’s been some controversy concerning the teams chosen to play for this year’s title, but they were determined by the computer, and who can question that?
TV: Whoa, Nelly! M.I.T. has fumbled the coin toss and Caltech goes wild!
One Researcher's Ouch
Courtesy Ben Toner, via a
math preprint by Craig Feinstein:
And the author welcomes and challenges anyone to produce a rigorous version, as he has no plans of even trying, because he is pretty tired of working on this problem and if he had to do it over again would never have even attempted it, not even for the prize of a million dollars for solving it – it’s just not worth all of the headache…
Life, Death, and the Meaning of it All
Well I will be away from blogging a bit. My dad (Larry) passed away suddenly last Friday at my family’s cabin in northern California. I’m now at home in Yreka among family and friends. Of course, normally this would be a depressing post, but there was little to nothing depressing about my father so instead I just wanted to write short notes on a few things which are very much Larry-esque.
1. Look up! When we go out at night, we just don’t spend time to look at the stars. Stop and look up at the sky (even if you can see but two stars because you live in a smog cloaked sky!) Stars remind us that we live in an amazing and wonderous universe. That those points of light are light years away and that we are small in this universe don’t diminish us but only put outselves in perspective of a greater grandeur. So look up at the stars! Spend an evening freezing yourself in a lawn chair and thinking about perspective. “As for myself, I know nothing with any certainty, but the sight of stars makes me dream.” Vincent van Gogh.
2. Find humor and amazement in everything you do. There is nothing which enforces a law of seriousness (well maybe brussel sprouts, but even then, they’re pretty comic, don’t you think?). The human predicament, even in its darkest times, must alway remain a comedy, or a tragecomedy, or at least a bit of learning from the astonishing places we get ourselves into. The trap is that we find ourselves believing our ideas and stuck viewing the world through a single lens. Use the lens of humor and amazement! Don’t take the world’s seriousness seriously!
So remember my dad these next few weeks: look up at the stars and find humor in new places!
Berkeley
From The Transmigration of Timothy Archer by Philip K. Dick:
Dreams of poverty excited universal enjoyment in Berkeley, coupled with the hope that the political and economic situation would worsen, throwing the country into ruin: this was the theory of the activists. Misfortune so vast that it would wreck everyone, responsible and not responsible alike sinking into defeat.