Please use this identifier to cite or link to this item: https://doi.org/10.1063/1.3672009
Title: Categorical tensor network states
Authors: Biamonte, J.D.
Clark, S.R. 
Jaksch, D. 
Issue Date: 2011
Citation: Biamonte, J.D., Clark, S.R., Jaksch, D. (2011). Categorical tensor network states. AIP Advances 1 (4) : -. ScholarBank@NUS Repository. https://doi.org/10.1063/1.3672009
Abstract: 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 ψ, we present a new and general method to factor |ψ 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. © 2011 Author(s).
Source Title: AIP Advances
URI: http://scholarbank.nus.edu.sg/handle/10635/115018
ISSN: 21583226
DOI: 10.1063/1.3672009
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