Fat Manifolds and Linear Connections
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Higher entropy enables classical information. Many of the coauthors in these breakthroughs are undergraduate students. Paper ; blog post end of July, A collection of equiangular lines is a collection of lines so that the angles between every pair of lines in the same? In Dom de Caen found for the first time an equiangular set of lines in space of size.
The crucial observation that one of the graphs in the Cameron—Seidel association scheme has a certain eigenvalue of large multiplicity. Prior to this construction, the largest sets had sizes of order. For another result by Dom, see this post. On the way they proved the following very interesting theorem. Theorem: A bounded degree graph must have sublinear second eigenvalue multiplicity. Paper , blog post end of June Abstract : We prove a conjecture of Fox, Huang, and Lee that characterizes directed graphs that have constant density in all tournaments: they are disjoint unions of trees that are each constructed in a certain recursive way.
On the nose! Let me copy its description from the paper:. Lately the conjecture has been proved for many families of though the conjecture remains open in general. In particular, the case is open. These are two remarkable papers by the same team of researchers. An earlier breakthrough on the problem was made by Zhao in when he was an undergraduate student.
Over the years I heard a lot of lectures and private explanation on upper tails and the remarkable related mathematics. But when I wrote the post I realized my knowledge is too sparse for giving a thorough description, and I decided not to wait and write a short post.
This post by Yufei describes some of the history very nicely as well as the major papers by Eyal and Yufei from and Skip to content. Posted on September 23, by Gil Kalai.
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Achieving quantum supremacy via sampling In the last decade there were several suggestions to demonstrate the computational superior power of quantum circuits via sampling tasks. Computing the ideal distribution D is computationally hard so as n increases you need a bigger and bigger computational effort to compute D. Earlier experiments The Google group itself ran this experiment for 9 qubits in The missing part in the experiment.
The main potential mistake and the matter of correlation. The general picture regarding correlated qubit errors is the following: 1 Errors for gated qubits for a CNOT gate are substantially positively correlated. My predictions. A problem with the supremacy statements itself. Distance-3 surface code In I was one of the organizers of a conference Qstart celebrating our then new Quantum Science Center.
Fat manifolds and linear connections / Alessandro De Paris, Alexandre Vinogradov - Details - Trove
The authors Whether it stands or refuted the Google paper represents serious multidisciplinary science, an important moment for the scientists involved in the project, a notable event in science, and a remarkable human triumph. Other links and updates Scott Aaronson enthusiastic blog post gives his take in the new development and also mentions some several key researchers behind the pursuit of quantum supremacy on NISQ systems. Share this: Facebook Reddit Twitter.
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Like this: Like Loading Posted on September 22, by Gil Kalai. An isoperimetric inequality for the Hamming cube and some consequences Abstract: Slightly modified. Discussion Counting independent sets in graphs and hypergraphs and related things. Posted on September 9, by Gil Kalai. A little more about the result It is still a major open problem to replace by and by ultra-flat polynomials.
The problem can be traced back to a paper by Hardy and Littlewood. Richard Ehrenborg with a polyhedron In the Problem session last Thursday in Oberwolfach, Steve Klee presented a beautiful problem of Richard Ehrenborg regarding the number of spanning trees in bipartite graphs. Posted on August 28, by Gil Kalai.
Posted in Combinatorics , Uncategorized 4 Comments. A short abstract for the lecture and the paper is: We give a computational complexity argument against the feasibility of quantum computers. Paper ; blog post end of July, A collection of equiangular lines is a collection of lines so that the angles between every pair of lines in the same? Here are two classical questions: What is the maximum number of equiangular lines in? Given an angle what is the maximum number of equiangular lines in? Impartial digraphs by Yufei Zhao and Yunkun Zhou. Paper , blog post end of June Abstract : We prove a conjecture of Fox, Huang, and Lee that characterizes directed graphs that have constant density in all tournaments: they are disjoint unions of trees that are each constructed in a certain recursive way.
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Blog post. Combinatorics and more. Create a free website or blog at WordPress. In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a?
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