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Rhythm is a Quantum Concatenated Code

I do believe this is the first time I’ve performed the paper dance on the scienceblogs incarnation of this blog. Yep, it’s that time again: it’s the paper dance!
“A far away light in the futuristic place we might be; It’s a tiny world just big enough to support the kingdom of one knowledgeable; I feel a wave of loneliness and head back down I’m going too fast (I’m going too fast)”

arXiv:0806.2160
The Stability of Quantum Concatenated Code Hamiltonians
Authors: D. Bacon
Abstract: Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to achieving this is via active quantum error correction using fault-tolerant techniques. An alternative to this approach is to engineer strongly interacting many-body quantum systems that enact the quantum error correction via the natural dynamics of these systems. Here we present a method for achieving this based on the concept of concatenated quantum error correcting codes. We define a class of Hamiltonians whose ground states are concatenated quantum codes and whose energy landscape naturally causes quantum error correction. We analyze these Hamiltonians for robustness and suggest methods for implementing these highly unnatural Hamiltonians.

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Drunkard's Tennis and the Advice of Winners

Writing grants and teaching, not to mention trying to get some actual research done, has taken up a considerable amount of my time this quarter. I mean, sheesh, I’ve barely had any time to read! This has, of course, made me grumpy. So when the publisher of The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow offered me a review copy of the book, I was very happy. I mean, I love probability and I love, um, well….you know 🙂
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School's Out For Summer…Almost

Today is the final exam for the course I’ve been teaching this summer. So I need some reading material for when I’m not watching the students take their exam. Here are two fun ones I just downloaded (one via Alea):

arXiv:0803.3913:
The Reverse of The Law of Large Numbers
Authors: Kieran Kelly, Przemyslaw Repetowicz, Seosamh macReamoinn
Abstract:The Law of Large Numbers tells us that as the sample size (N) is increased, the sample mean converges on the population mean, provided that the latter exists. In this paper, we investigate the opposite effect: keeping the sample size fixed while increasing the number of outcomes (M) available to a discrete random variable. We establish sufficient conditions for the variance of the sample mean to increase monotonically with the number of outcomes, such that the sample mean “diverges” from the population mean, acting like an “reverse” to the law of large numbers. These results, we believe, are relevant to many situations which require sampling of statistics of certain finite discrete random variables.

and

arXiv:0806.0485
Complex and Unpredictable Cardano
Aurthor: Artur Ekert
Abstract: This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated to Giuseppe Castagnoli on the occasion of his 65th birthday. Back in the early 1990s, Giuseppe instigated a series of meetings at Villa Gualino, in Torino, which brought together few scattered individuals interested in the physics of computation. By doing so he effectively created and consolidated a vibrant and friendly community of researchers devoted to quantum information science. Many thanks for that!

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George Soros Meets Kochen-Specker

I’ll admit it: I like reading George Soros’ books. I mean, here’s a guy whose made a godzillion dollars in the financial markets, has been behind political destabilizations/stabilizations worldwide, taken on a U.S. president (can you guess which one?), and yet, in spite of this, can write a book in which he talks his own brand of….philosophy and how it relates to life, the universe, and the current financial crisis. Whah?
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Blackberry Hole Grows Larger

Blessed be Mike Lazaridis:

Waterloo, Ontario, Canada, June 4, 2008 – In a new and generous act of personal philanthropy, Mike Lazaridis has provided an additional $50 million (Canadian) to Perimeter Institute for Theoretical Physics (PI). This private donation increases his personal contributions to $150 million in the research institute.

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Teaching Generalizations of Probability

Hoisted from the comments, Robin asks:

So, with that in mind, here’s a question. What do you think about teaching quantum mechanics as noncommutative probability theory? In other words, by starting with probability theory and alluding to probabilistic mechanics (e.g., distributions on phase space), and then introducing quantum theory as a generalization of probability.
This is how I think of quantum theory all the time now — and it makes tremendous sense to me. I think it’s how I want to teach it. And I’m curious what y’all think.

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