Topological Data Analysis of Quantum State Tomography

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Quantum state tomography (QST) is a crucial technique for characterizing the state of a quantum system. However, the data generated by QST—typically a large, dense measurement matrix—presents significant challenges for analysis and interpretation. This work proposes a novel approach leveraging Topological Data Analysis (TDA), specifically persistent homology, to extract meaningful insights from these complex quantum state data. We demonstrate that the underlying topological structure of the measurement matrices can reveal fundamental characteristics of the quantum state, including entanglement properties and the degree of coherence. The core idea involves treating the measurement matrix as a high-dimensional point cloud and applying persistent homology to uncover persistent loops and connected components, which directly correspond to topological features of the quantum state. This method offers a new perspective on QST data analysis, potentially leading to improved state characterization and a deeper understanding of quantum entanglement. The application of TDA provides a robust and geometric interpretation of the measurement data, moving beyond traditional statistical methods.

DOI: 10.5281/zenodo.22637069

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