Spectroscopic Search for Topological Protection in Open Quantum Hardware: The Dissipative Mixed Hodge Module Approach

• URL: http://arxiv.org/abs/2512.21662v1
• Date: Thu, 25 Dec 2025 13:06:42 GMT
• Title: Spectroscopic Search for Topological Protection in Open Quantum Hardware: The Dissipative Mixed Hodge Module Approach
• Authors: Prasoon Saurabh,
• Abstract summary: Standard protocols model the dynamics of open quantum systems as a superposition of isolated, exponentially decaying eigenmodes.<n>We resolve this ambiguity by introducing a geometric framework based on textitDissipative Mixed Hodge Modules (DMHM)<n>We demonstrate that WFS acts as a dissipative x-ray, quantifying dissipative leakage in molecular polaritons and certifying topological isolation in Non-Hermitian Aharonov-Bohm rings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Standard spectroscopic protocols model the dynamics of open quantum systems as a superposition of isolated, exponentially decaying eigenmodes. This paradigm fails fundamentally at Exceptional Points, where the eigenbasis collapses and the response becomes dominated by non-diagonalizable Jordan blocks. We resolve this ambiguity by introducing a geometric framework based on \textit{Dissipative Mixed Hodge Modules} (DMHM). By replacing the scalar linewidth with a topological \textit{Weight Filtration}, we derive ``Weight Filtered Spectroscopy'' (WFS)--a protocol that spatially separates decay channels based on the nilpotency rank of the Liouvillian. We demonstrate that WFS acts as a dissipative x-ray, quantifying dissipative leakage in molecular polaritons and certifying topological isolation in Non-Hermitian Aharonov-Bohm rings. This establishes that topological protection persists as an algebraic invariant even when the spectral gap is closed.

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