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arXiv:2609.27318

Minimal representations of topology-preserving quantum-like states

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

quant-phmath.COSubmitted Sep 23, 2026• Announced Sep 24, 2026• 0 citations
v1 · Sep 23, 2026v2 · Oct 6, 2026
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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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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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