Categorical Tensor Network States

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

Research output: Contribution to journalArticle

22 Citations (Scopus)
203 Downloads (Pure)

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.
Original languageEnglish
Article number042172
Number of pages39
JournalAIP Advances
Volume1
Issue number4
DOIs
Publication statusPublished - 2 Dec 2010

Keywords

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

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    Biamonte, J. D., Clark, S. R., & Jaksch, D. (2010). Categorical Tensor Network States. AIP Advances, 1(4), [042172]. https://doi.org/10.1063/1.3672009