| Résumé: | <p>We examine the use of the mathematics of category theory in the description<br/> of quantum states by tensor networks. This approach enables the development of<br/> a categorical framework allowing a solution to the quantum decomposition<br/> problem. Specifically, given an n-body quantum state ψ, we present<br/> a general method to factor ψ into a tensor network. Moreover, this<br/> decomposition of ψ uses building blocks defined mathematically in<br/> terms of purely diagrammatic laws. We use the solution to expose a previously<br/> unknown and large class of quantum states which we prove can be sampled<br/> efficiently and exactly. This general framework of categorical tensor network<br/> states, where a combination of generic and algebraically defined tensors<br/> appear, enhances the theory of tensor network states.</p> <p> </p> <p>Blogs about this paper:</p> <p>(i) <a href='\"http://golem.ph.utexas.edu/category/2010/09/bimonoids_from_biproducts.html\"'>http://golem.ph.utexas.edu/category/2010/09/bimonoids_from_biproducts.html</a></p> <p>(ii) <a href='\"http://johncarlosbaez.wordpress.com/2010/09/29/jacob-biamonte-on-tensor-networks/\"'>http://johncarlosbaez.wordpress.com/2010/09/29/jacob-biamonte-on-tensor-networks/</a> </p> <p>Talks about this paper:</p> <p>(i) <a href='\"http://new.iqc.ca/news-events/calendar/generated/jacob-biamonte-2010-12-2\"'>http://new.iqc.ca/news-events/calendar/generated/jacob-biamonte-2010-12-2</a> (IQC, <span black;\"="" style='\"color:'>Institute for Quantum Computing<br/> University of Waterloo, Canada)</span></p> <p>Link to arXiv version:</p> <p>* <a href='\"http://arxiv.org/abs/1012.0531\"'>http://arxiv.org/abs/1012.0531</a></p>
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