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PreprintarXiv licencearXiv

Minimal representations of topology-preserving quantum-like states

  • William Horvat
  • Debadrita Saha
  • Nicolás Gigena
  • Prineha Narang
  • Gregory D. Scholes
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Abstract

We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from quantum-like bits that preserves the relevant spectral and topological properties. We show that this result follows from the fact that the operations of taking the Cartesian product of graphs and constructing equitable partition of the graphs commute. Numerical simulations illustrate the preserved emergent eigenstates in the reduced structures. Additionally, we provide a construction of the minimal structure without passing through the Cartesian product. Finally, we frame quantum-like structures in the language of topology and fibrations.

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Cite

BibTeXRIS
BibTeX
@misc{horvat2026minimal,
  title = {{Minimal representations of topology-preserving quantum-like states}},
  author = {William Horvat and Debadrita Saha and Nicolás Gigena and Prineha Narang and Gregory D. Scholes},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.27318},
  eprint = {2609.27318},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27318},
}
RIS
TY  - UNPB
TI  - Minimal representations of topology-preserving quantum-like states
AU  - William Horvat
AU  - Debadrita Saha
AU  - Nicolás Gigena
AU  - Prineha Narang
AU  - Gregory D. Scholes
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.27318
UR  - https://arxiv.org/abs/2609.27318
AB  - We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from quantum-like bits that preserves the relevant spectral and topological properties. We show that this result follows from the fact that the operations of taking the Cartesian product of graphs and constructing equitable partition of the graphs commute. Numerical simulations illustrate the preserved emergent eigenstates in the reduced structures. Additionally, we provide a construction of the minimal structure without passing through the Cartesian product. Finally, we frame quantum-like structures in the language of topology and fibrations.
ER  -