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If Quantum Computers are not Possible Why are Classical Computers Possible? | Combinatorics and more
As most of my readers know, I regard quantum computing as unrealistic. You can read more about it in my Notices AMS paper and its extended version (see also this post) and in the discussion of Puzzle 4 from my recent puzzles paper (see also this post). The amazing progress and huge investment in quantum computing (that I presented and update  routinely in this post) will put my analysis to test in the next few years.
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november 2017 by nhaliday
Quantum Supremacy: Office of Science and Technology Policy QIS Forum, Eisenhower Executive Office Building, White House Complex, Washington DC, October 18, 2016. Another version at UTCS Faculty Lunch, October 26, 2016. Another version at UT Austin Physics Colloquium, Austin, TX, November 9, 2016.

Complexity-Theoretic Foundations of Quantum Supremacy Experiments: Quantum Algorithms Workshop, Aspen Center for Physics, Aspen, CO, March 25, 2016

When Exactly Do Quantum Computers Provide A Speedup?: Yale Quantum Institute Seminar, Yale University, New Haven, CT, October 10, 2014. Another version at UT Austin Physics Colloquium, Austin, TX, November 19, 2014; Applied and Interdisciplinary Mathematics Seminar, Northeastern University, Boston, MA, November 25, 2014; Hebrew University Physics Colloquium, Jerusalem, Israel, January 5, 2015; Computer Science Colloquium, Technion, Haifa, Israel, January 8, 2015; Stanford University Physics Colloquium, January 27, 2015
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may 2017 by nhaliday
Dvoretzky's theorem - Wikipedia
In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck. In essence, it says that every sufficiently high-dimensional normed vector space will have low-dimensional subspaces that are approximately Euclidean. Equivalently, every high-dimensional bounded symmetric convex set has low-dimensional sections that are approximately ellipsoids.

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january 2017 by nhaliday

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