Categorical Tensor Network States

Jacob D. Biamonte, Stephen R. Clark, Dieter Jaksch

Research output: Contribution to journalArticle (Academic Journal)peer-review

27 Citations (Scopus)


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.
Original languageEnglish
Article number042172
JournalAIP Advances
Publication statusPublished - 12 Dec 2011

Bibliographical note

39 pages, 31 figures, published version


  • quant-ph
  • cond-mat.other
  • cs.CC
  • cs.LO
  • math-ph
  • math.MP


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