Categorical Tensor Network States

Details Categorical Tensor Network States Categorical Tensor Network States

2010-12-02

arxiv.org/abs/1012.0531v2

AIP Advances 1(4), 042172 (2011)

Physics

Quantum Physics

39 pages, 31 figures, published version

Scientific paper

10.1063/1.3672009

We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state S, we present a new and general method to factor S into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can 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.

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