Minimal representations of topology-preserving quantumlike states

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

doi:10.1103/4kcg-z9v2

Minimal representations of topology-preserving quantumlike states

William Horvat ^1,*, Debadrita Saha ^2,*, Nicolás Gigena³, Prineha Narang¹, and Gregory D. Scholes ²

¹College of Letters and Science, University of California, Los Angeles, California 90095, USA
²Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³CONICET-Departamento de Física, Universidad Nacional de La Plata, C.C. 67, 1900 La Plata, Argentina

^*These authors contributed equally to this work.

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Phys. Rev. E 114, 044326 – Published 28 October, 2026

DOI: https://doi.org/10.1103/4kcg-z9v2

Abstract

We provide an equitable partition that gives an exact, minimal representation for the graph Cartesian product formed from quantumlike 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 quantumlike structures in the language of topology and fibrations.

Physical Review E

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Minimal representations of topology-preserving quantumlike states

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