Research

Categorical Tensor Network States


Reference:

Biamonte, J. D., Clark, S. R. and Jaksch, D., 2010. Categorical Tensor Network States. AIP Advances, 1, 042172.

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    Official URL:

    http://dx.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 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.

    Details

    Item Type Articles
    CreatorsBiamonte, J. D., Clark, S. R. and Jaksch, D.
    DOI10.1063/1.3672009
    Uncontrolled Keywordsquant-ph,cond-mat.other,cs.cc,cs.lo,math-ph,math.mp
    DepartmentsFaculty of Science > Physics
    RefereedYes
    StatusPublished
    ID Code47359
    Additional Information39 pages, 31 figures, published version

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