Category Archives: Physics

Aaronson and Arkhipov’s Result on Hierarchy Collapse

Scott Aaronson gave a thought-provoking lecture in our Theory seminar three weeks ago.  (Actually, this was eleven months ago.) The slides are here . The lecture discussed two results regarding the computational power of quantum computers. One result from this paper gives an … Continue reading

Posted in Computer Science and Optimization, Physics, Quantum | Tagged , , , , , | 10 Comments

Octonions to the Rescue

Xavier Dahan and Jean-Pierre Tillich’s Octonion-based Ramanujan Graphs with High Girth. Update (February 2012): Non associative computations can be trickier than we expect. Unfortunately, the paper by Dahan and Tillich turned out to be incorrect. Update: There is more to … Continue reading

Posted in Algebra and Number Theory, Combinatorics, Computer Science and Optimization, Open problems, Physics | Tagged , , , | 11 Comments

Benoît’s Fractals

Mandelbrot set Benoît Mandelbrot passed away a few dayes ago on October 14, 2010. Since 1987, Mandelbrot was a member of the Yale’s mathematics department. This chapterette from my book “Gina says: Adventures in the Blogosphere String War”   about fractals is brought here on this … Continue reading

Posted in Geometry, Obituary, Physics, Probability | 6 Comments

Itamar Pitowsky: Probability in Physics, Where does it Come From?

I came across a videotaped lecture by Itamar Pitowsky given at PITP some years ago on the question of probability in physics that we discussed in two earlier posts on randomness in nature (I, II). There are links below to … Continue reading

Posted in Obituary, Philosophy, Physics, Probability | Tagged , , , | 1 Comment

Randomness in Nature II

In a previous post we presented a MO question by Liza about randomness:  What is the explanation of the apparent randomness of high-level phenomena in nature? 1. Is it accepted that these phenomena are not really random, meaning that given enough … Continue reading

Posted in Philosophy, Physics, Probability | Tagged , , , | 16 Comments

When Noise Accumulates

I wrote a short paper entitled “when noise accumulates” that contains the main conceptual points (described rather formally) of my work regarding noisy quantum computers.  Here is the paper. (Update: Here is a new version, Dec 2010.) The new exciting innovation in computer … Continue reading

Posted in Computer Science and Optimization, Physics, Quantum | Tagged , , , | 9 Comments

Detrimental Noise

 “Imagine there’s no heaven, it’s easy(?) if you try,” John Lennon   Disclaimer: It is a reasonable belief  (look here, and here), and an extremely reasonable working assumption (look  here) that computationally superior quantum computers can be built.  (This post and the draft … Continue reading

Posted in Computer Science and Optimization, Controversies and debates, Physics, Quantum | Tagged , , , | 1 Comment