Quantum Simulation of Abstract Algebra

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

This paper explores the potential of quantum simulation to revolutionize the modeling of abstract algebra, addressing limitations of classical approaches. We propose a novel quantum algorithm, Quantum Lattice Construction, designed to iteratively construct and analyze algebraic structures, employing quantum superposition and entanglement to represent and manipulate algebraic concepts. The core claim is that this approach offers a fundamentally new path towards more accurate and efficient abstract algebra representation and analysis. We outline the algorithm's design, discuss its potential benefits, and present preliminary results demonstrating its effectiveness in a simplified example. The paper concludes with an assessment of the challenges and future directions for this research.

DOI: 10.5281/zenodo.22329070

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