We have a special group meeting Thursday December 9, 2010 at 1pm by a visitor to our group, Jacob D. Biamonte, from the Oxford University Computing Laboratory. The location is Pfizer Lecture Hall Pfizer Lecture Hall in Mallinckrodt Laboratory. *Title:* Categorical Tensor Network States *Abstract:* *I plan to present results from a study in the use of the mathematics of category theory in the description of quantum states by tensor networks. This approach enables the development of a categorical framework allowing a solution to the quantum decomposition problem. Specifically, given an n-body quantum state S, we found a general method to factor S into a tensor network. Moreover, this decomposition of S uses building blocks defined mathematically in terms of purely diagrammatic laws. We used the solution to expose a previously unknown and large class of quantum states which we prove to be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states. Part's of my talk will represent joint work with Stephen R. Clark (CQT, Kebble College, Oxford) and Dieter Jaksch (Oxford, Kebble College, CQT). *