Uniform matrix product states from an algebraic geometer's point of view

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Date
2023
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Czapliński, Adam
Seynnaeve, Tim
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10.1016/j.aam.2022.102417
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Advances in Applied Mathematics ; 142 (2023). - 102417. - Elsevier. - ISSN 0196-8858. - eISSN 1090-2074
Abstract
We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equations and identifiability. By an interplay of theorems from algebra, geometry and quantum physics we answer several questions and conjectures posed by Critch, Morton and Hackbusch.
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510 Mathematics
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ISO 690CZAPLIŃSKI, Adam, Mateusz MICHALEK, Tim SEYNNAEVE, 2023. Uniform matrix product states from an algebraic geometer's point of view. In: Advances in Applied Mathematics. Elsevier. 142, 102417. ISSN 0196-8858. eISSN 1090-2074. Available under: doi: 10.1016/j.aam.2022.102417
BibTex
@article{Czaplinski2023Unifo-58629,
  year={2023},
  doi={10.1016/j.aam.2022.102417},
  title={Uniform matrix product states from an algebraic geometer's point of view},
  volume={142},
  issn={0196-8858},
  journal={Advances in Applied Mathematics},
  author={Czapliński, Adam and Michalek, Mateusz and Seynnaeve, Tim},
  note={Article Number: 102417}
}
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