The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper bound is given in cases relevant for applications such as varieties of matrix product states and projected entangled pairs states. We provide a range (the "supercritical range") of the parameters where the upper bound is sharp.

Dimension of tensor network varieties / Bernardi, A.; De Lazzari, C.; Gesmundo, F.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 2022:(2022), pp. 225005901-225005931. [10.1142/S0219199722500596]

Dimension of tensor network varieties

Bernardi A.;De Lazzari C.
;
2022-01-01

Abstract

The tensor network variety is a variety of tensors associated to a graph and a set of positive integer weights on its edges, called bond dimensions. We determine an upper bound on the dimension of the tensor network variety. A refined upper bound is given in cases relevant for applications such as varieties of matrix product states and projected entangled pairs states. We provide a range (the "supercritical range") of the parameters where the upper bound is sharp.
2022
Bernardi, A.; De Lazzari, C.; Gesmundo, F.
Dimension of tensor network varieties / Bernardi, A.; De Lazzari, C.; Gesmundo, F.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 2022:(2022), pp. 225005901-225005931. [10.1142/S0219199722500596]
File in questo prodotto:
File Dimensione Formato  
s0219199722500596.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 689.32 kB
Formato Adobe PDF
689.32 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/372549
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact