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Unifying Classical Spin Models Using A Quantum Formalism

University of British Columbia. Department of Physics and Astronomy; Workshop on Quantum Algorithms, Computational Models and Foundations of Quantum Mechanics; Pacific Institute for the Mathematical Sciences; Summer School on Quantum Information (10th : 2010 : Vancouver, B.C.)

We have recently shown that the partition function of any classical spin model, including all discrete standard statistical models and all Abelian discrete lattice gauge theories, can be expressed as the specific instance of the partition function of a four dimensional Ising lattice gauge theory. This unifies models with apparently very different features (global vs. local symmetries, many body interactions, different dimensions, etc) in a single complete model. The proof of the result uses techniques from quantum information. In this talk we review these mappings and discuss recent developments, including quantum algorithms to approximate the partition function.

Text

2016-11-22

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/30936

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/