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Quantum Simulation

Minimal representations of topology-preserving quantum-like states

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

Year

2026

Paper ID

81856

Status

Preprint

Abstract Read

~2 min

Abstract Words

93

Citations

N/A

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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2609.27318 [2] arXiv https://arxiv.org/abs/2609.27318 [3] Publisher https://arxiv.org/abs/2609.27318

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External citation index: OpenAlex citation signal

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