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Quantum State Preparation Representation

Triangular tensor networks, pencils of matrices and beyond

arXiv
Authors: Alessandra Bernardi, Fulvio Gesmundo

Year

2026

Paper ID

767

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors as pencils of matrices. We provide a complete characterization of these varieties in terms of the Kronecker invariants of pencils. We determine their dimension, identifying the cases for which the dimension is smaller than the expected parameter count. We provide necessary conditions for membership in these varieties, in terms of the geometry of classical determinantal varieties, coincident root loci and plane cubic curves. We address some extensions to arbitrary graphs.

Why This Paper Matters

  • This paper contributes to the Quantum State Preparation & Representation research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.15114 [2] arXiv https://arxiv.org/abs/2602.15114 [3] Publisher https://arxiv.org/abs/2602.15114

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