[QIP-Sem] Jacob D. Biamonte, Categorical Tensor Network States, 1pm, Harvard

[J D Whitfield]

*Speaker:*
Jacob D. Biamonte, from the Oxford University Computing Laboratory

*Title:*
Categorical Tensor Network States

*Location:*
*Pfizer Lecture Hall in Mallinckrodt Laboratory (12 Oxford St, Cambridge,
MA).*

*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,
Keble College, Oxford) and Dieter Jaksch (Oxford, Keble College, CQT). *
*
*
*Based on arxiv:1012.0531 <http://arxiv.org/abs/1012.0531>.*
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