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PreprintCC BY 4.0Zenodo

[07]Deterministic Geometric Decoupling Blocks Operator Krylov Complexity and Enables Multi-Channel Chaos Isolation

  • Wenjun Luo1
  1. 1Independent Researcher
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Abstract

Krylov complexity is a central metric for characterizing quantum chaos and operator scrambling. Here, we propose a purely geometric connectivity-engineering scheme: by reconstructing the spin chain topology with a fixed hopping step, the parent system is strictly decoupled into multiple independent sub-chains. Numerically, the complexity of local operators in the normal chain grows rapidly, whereas in the decoupled network, it is strictly bounded and undergoes periodic revivals at low dimensions. The rapid decay of Lanczos coefficients and the drop in Krylov entropy confirm that the geometric-induced direct sum decomposition of the Hilbert space causes the Lanczos generation chain to truncate sharply beyond a finite order (the "wall effect"). This mechanism, analogous to a topological firewall in holographic gravity, challenges the connectivity assumption of the Universal Operator Growth Hypothesis and provides a minimalist deterministic benchmark for chaos isolation and information shielding in multi-core quantum chips.

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Cite

BibTeXRIS
BibTeX
@misc{luo202607deterministic,
  title = {{[07]Deterministic Geometric Decoupling Blocks Operator Krylov Complexity and Enables Multi-Channel Chaos Isolation}},
  author = {Wenjun Luo},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23622999},
  url = {https://zenodo.org/records/23622999},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - [07]Deterministic Geometric Decoupling Blocks Operator Krylov Complexity and Enables Multi-Channel Chaos Isolation
AU  - Wenjun Luo
PY  - 2026
DA  - 2026/10/24
PB  - Zenodo
DO  - 10.5281/zenodo.23622999
UR  - https://zenodo.org/records/23622999
AB  - Krylov complexity is a central metric for characterizing quantum chaos and operator scrambling. Here, we propose a purely geometric connectivity-engineering scheme: by reconstructing the spin chain topology with a fixed hopping step, the parent system is strictly decoupled into multiple independent sub-chains. Numerically, the complexity of local operators in the normal chain grows rapidly, whereas in the decoupled network, it is strictly bounded and undergoes periodic revivals at low dimensions. The rapid decay of Lanczos coefficients and the drop in Krylov entropy confirm that the geometric-induced direct sum decomposition of the Hilbert space causes the Lanczos generation chain to truncate sharply beyond a finite order (the "wall effect"). This mechanism, analogous to a topological firewall in holographic gravity, challenges the connectivity assumption of the Universal Operator Growth Hypothesis and provides a minimalist deterministic benchmark for chaos isolation and information shielding in multi-core quantum chips.
ER  -