Title: Meta-Morphing of Abstract Algebra via Quantum Simulation

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

Abstract algebra, a cornerstone of mathematics, provides a powerful framework for studying algebraic structures and their properties. Traditionally, this field relies heavily on manual analysis and conjecture-driven exploration. This paper proposes a novel approach using quantum simulation to automate and precisely map abstract algebraic structures to physical systems. We introduce a quantum framework that allows for the rapid and accurate exploration of algebraic relationships, revealing patterns and relationships that are currently inaccessible to classical methods. The core mechanism involves leveraging quantum algorithms to simulate the evolution of algebraic structures, generating a vast amount of data that can be analyzed for new mathematical objects. This research aims to significantly accelerate the discovery process, potentially leading to breakthroughs in areas such as symmetry theory, group theory, and the understanding of complex numbers.

DOI: 10.5281/zenodo.22297891

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