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Quantum State Preparation Representation

Quotient geometry of tensor ring decomposition

arXiv
Authors: Bin Gao, Renfeng Peng, Ya-xiang Yuan

Year

2026

Paper ID

3125

Status

Preprint

Abstract Read

~2 min

Abstract Words

103

Citations

N/A

Abstract

Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods. Despite the practical success of the tensor ring (TR) decomposition, its intrinsic geometry remains less understood, primarily due to the underlying ring structure and the resulting nontrivial gauge invariance. We establish the quotient geometry of TR decomposition by imposing full-rank conditions on all unfolding matrices of the core tensors and capturing the gauge invariance. Additionally, the results can be extended to the uniform TR decomposition, where all core tensors are identical. Numerical experiments validate the developed geometries via tensor ring completion tasks.

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.
  • Differential geometries derived from tensor decompositions have been extensively studied and provided the foundations for a variety of efficient numerical methods.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2601.21874 [2] arXiv https://arxiv.org/abs/2601.21874 [3] Publisher https://arxiv.org/abs/2601.21874

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