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Topological Quantum Computing

Topological Orders from Reflection Positive Frustration-free Hamiltonians

arXiv
Authors: Zhengwei Liu, Zishuo Zhao

Year

2025

Paper ID

50836

Status

Preprint

Abstract Read

~2 min

Abstract Words

77

Citations

N/A

Abstract

We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems. For any reflection positive frustration-free Hamiltonian, We proved that the local topological quantum order (LTQO) condition of ground states on a disk holds if and only if the ground state on the sphere is non-degenerate. Furthermore, we show that the Osterwalder-Schrader reconstruction produces the boundary local net of operator algebras from the local ground states.

Why This Paper Matters

  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
  • It adds a 2025 reference point for readers tracking recent quantum research.
  • We establish a framework with reflection positivity as the first principle for establishing the boundary theory of topologically ordered quantum spin systems.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2510.20662 [2] arXiv https://arxiv.org/abs/2510.20662 [3] Publisher https://arxiv.org/abs/2510.20662

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