Quantum Spectral Geometry Literature Review: Laplace–Beltrami Harmonics and SU(3) Qutrit Information

Trent Slade

Published Dec 3, 2025• 0 citations

Abstract

This review investigates deep structural links between spectral geometry on curved manifolds and the architecture of qutrit-based quantum information. Focusing on Laplace–Beltrami operators, harmonic spectra, and eigenfunction structures on complex projective spaces such as ℂP², the study surveys how geometric mode families encode ternary logic, SU(3) representations, and qutrit control protocols. The analysis integrates differential geometry, representation theory, and quantum control, highlighting that SU(3) qutrit dynamics can often be interpreted as discrete manifestations of continuous geometric symmetries. Special attention is given to Gell-Mann generators, coherent-state constructions, spectral gaps, and geometric phases. Across the surveyed literature, a unifying theme emerges: the eigenstructure of curved manifolds provides both the natural harmonic basis and the dynamical substrate for triadic quantum information processing.

DOI: 10.5281/zenodo.17797342

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