Complexity, Entropy, and the Physics of Information Lecture Series
Wednesday, November 10, 2004, 5:00 PM. Refreshments 4:15 PM.
Robert N. Noyce Conference Room, Santa Fe Insitute
Wim van Dam
Computer Science Dept., University of California, Santa Barbara
Quantum Computing, Zeroes of Zeta Functions & Approximate Counting
Abstract:
In this talk I describe a possible connection between quantum computing and Zeta functions of finite field equations that is inspired by the ‘spectral approach’ to the Riemann conjecture. The assumption is that the zeroes of such Zeta functions correspond to the eigenvalues of finite dimensional unitary operators of natural quantum mechanical systems. To model the desired quantum systems I use the notion of universal, efficient quantum computation.
Using eigenvalue estimation, such quantum systems are able to approximately count the number of solutions of the specific finite field equations with an accuracy that does not appear to be feasible classically. For certain equations (Fermat hypersurfaces) I show that one can indeed model their Zeta functions with efficient quantum algorithms, which gives some evidence in favour of the proposal.
Alice, Bob, and …
In cryptography there has been a long tradition of calling two parties involved in a protocol Alice and Bob. This tradition has been proudly maintained in quantum information science, no doubt in large part because quantum cryptography was one of the first ideas in quantum information science. One of the nicest things about the Alice/Bob labeling scheme is that it allows one to use gender to distinguish parties. I suspect that since gender is dear to our animal hearts, this concise way of refering to parties has significant syntactic advantage. David Mermin once said something along the lines of “if quantum information contributes nothing else to physics it least it will have given us Alice and Bob.” Actually, where I’ve found the Alice/Bob labeling scheme most efficient is in special relativity where it allows one to give gender to different reference frames (note also that since all frames are equal…) It is much clearer to most students when you refer to “his reference frame” or “her reference frame.”
Along these lines, when you have to introduce a new party, it is traditional to call this party Eve. This is usually done because in cryptography, Eve is the eavesdroping malicious third party. But this screws up the whole gender roles efficient labeling. I therefore propose that instead of calling the third party Eve, we should call the third party E.T., or Elephant, or Eagle such that we can use “it” to refer to this party. Now what do we do for four parties?
Day One
Yesterday I drove the 3+ hours to Wolf Creek in Colorado to go skiing. And boy was it worth it! While Wolf Creek doesn’t yet have great coverage, most of the mountain was open, and, if you worked for it, you could still large stashes of untracked powder. If they get about another 18 inches they will be in great condition.
My most notable episode was an epic crash I had in the powder. I had climbed up this ridgeline to get to some nice steep tree lined runes with about a foot and a half of powder. It was a super nice day, very hot, and so I wasn’t wearing any gloves. I took off down the run and after about 5 turns I may a spectacular nosedive into the pow. Standing up, I was covered in powder and my hands were freezing cold. I mean really really freezing cold. It was at this moment that I realized that I was dehydrated from both the high altitude and the long climb I had made to reach the stash. Doh. Taking off my glasses was my next smart move. The next few seconds I could feel myself get light headed and thought “Headline: Santa Fe postdoc proves that even with a Ph.D. you can still be a moron.” After a few moments chilling in the sun, however, I recovered and promptly went to buy a Gatorade. Earlier in the morning I had noticed how many people were wearing packs for carrying water. I thought that was kind of funny, but now I think I’m going to go buy one.
An Amazing Histogram
For all political junkies this study of the 2004 presidential election by Michael Gastner, Cosma Shalizi, and Mark Newman is extremely interesting.
Update: It seems that the authors have gotten rid of the final histogram which claimed that 302 counties voted nearly fully for Kerry (IIRC >90% of the vote for Kerry.) This was the most interesting part of the article, unfortunately. Still an interesting article, but not nearly as shocking.
Welcome to Theocracy
Let’s give a warm welcome to the world’s latest theocracy, the United Christian States of America! All hail our new Commander and Pope, George Bush. Shall we kiss his ring?
On November Second, we learned that over fifty percent of America is totally and completely irrational. Don’t believe me? Go ask that epitome of rationality, a scientist. I know only two scientists who voted for George Bush, out of a sample of a few hundred. This election wasn’t a referendum on George Bush’s first term, as many a pundit would claim, because there is no rational way to argue that his term has been anything but a disaster. Don’t believe me? Ask a scientist. So the reason over fifty percent of America voted for the George Bush must be something a scientist cannot comprehend, and indeed it was: that bastion of irrationaly, religion. Ever tried to argue about the theory of evolution with a member of the religious right? Feel strangely familiar to arguing with a Bush supporter? Indeed.
Hearing the election results on November 2nd, the first thought which crossed my mind was that I wished that those who have not educated themselves enough to be able to put a rational thought together were banned from enjoying the benefits of the brilliant scientists who have advanced society. But that thought is too harsh. Instead, we must think about how to turn that irrational fifty percent into rational coherent human beings. It’s surely one of the reasons I want to end up as a teaching professor. And you, my dear audience, you a bastion of rationality, you should not shrink in expressing your disdain for the irrational. Let us drive out the idiot out of America, not by physically revolting, but by teaching America how to think coherently.
The Hollow Men
Roger Water’s Perfect Sense Part I:
The monkey sat on a pile of stones
And stared at the broken bone in his hand
And the stains of a Viennese quartet
Rang out across the land
The monkey looked up at the stars
And thought to himself
Memory is a stranger
History is for fools
And he cleaned his hands
In a pool of holy writing
Turned his back on the garden
And set out for the nearest town
Hold on hold on soldier
When you add it all up
The tears and the marrowbone
There’s an ounce of gold
And an ounce of pride in each ledger
And the Germans killed the Jews
And the Jews killed the Arabs
And the Arabs killed the hostages
And that is the news
And is it any wonder
That the monkey’s confused
He said Mama Mama
The President’s a fool
Why do I have to keep reading
These technical manuals
And the joint chiefs of staff
And the brokers on Wall Street said
Don’t make us laugh
You’re a smart kid
Time is linear
Memory is a stranger
History is for fools
Man is a tool in the hands
Of the great God Almighty
And they gave him command
Of a nuclear submarine
And sent him back in search of
The Garden of Eden
Voting
In from the brisk 26 degree cold, when was the last time I’ve been in a Parish building? 200 feet away, through the window, the MoveOn heard stands freezing their rears in the hopes of changing one last mind? Precinct 26 or 27? Look at my card, whooop, I’m 26, so there’s no line. No line to stand in, instead there is the infamous line of the aged volunteers ready to check me in. Yep, I’m in the book, says middle aged woman number one bedecked in her red, white, and blue sweat shirt. The grandma one over has me put my John Hancock on a line. But mine isn’t nearly as loud and shouting and revolutionary. Then its to the booth where a mighty poster board of choices await my decision. Green lights flicker as I consult my list of choices. Kerry for president. 1 Republican for my dad. 2 Greens for revolution. And then the lonely button to cast my vote is pressed. The lights go out and bits go somewhere hopefully safe from tamper. And back out into the 26 degree morning. 26. Huh. Hopefully a lucky number.
Quantum Catholic
Let it be known, to the legions of Catholic readers of this blog, that the Quantum Pontiff endorses John Kerry over George Bush in the United States presidential election. That’s right, you heard it here first, the (*ahem* Quantum) Pope endorses John Kerry!
Where's Da Moon?
Happy Lunar Eclipse! I was born on a lunar eclipse. Kind of explains things, doesn’t it?
Also: Is it a coincidence that the lunar eclipse happens to be on the night the Red Sox finally beat the curse? Also notice: Cardinals are as Red as they get. An omen for Nov. 2? I’ll take any ounce of hope I can get.
Augmented Reality
This lunch I saw a talk about “Augmented Reality” which is like virtual reality, except that you use a combination of the real world and VR type equipment to add new elements to the real world. Thus, for instance, users wear transparent displays so that they see extra objects in their environment. At the end of the talk, the discussion turned to using such a system for gaming. Think of playing Doom with your own home and neighborhood as the actual physical setting. Right now, like all things VR, however, the equipment is just too damn expensive.
But it got me thinking about a gaming system along these lines, but maybe not as expensive. Imagine a handheld LCD screen with a camera attached. You hold the system in front of you and it shows you a display. Now this display is a combination of the real physical world around you and augmented reality elements. Now imagine a first person shooting game, for example. You and your friends running around shooting each other through these hand held screens. Sound like fun?