Work

Minimal representations of topology-preserving quantumlike states

Year: 2026

Type: article

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.

Source: Physical review. E

DOI: 10.1103/4kcg-z9v2

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

Institutions: University of California, Los Angeles, Princeton University, Universidad Nacional de La Plata

Language: English

Topic: Graph theory and applications

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green