Machine Learning approach to reconstruct Density Matrices from Quantum Marginals

• URL: http://arxiv.org/abs/2410.11145v3
• Date: Wed, 01 Oct 2025 20:41:15 GMT
• Title: Machine Learning approach to reconstruct Density Matrices from Quantum Marginals
• Authors: Daniel Uzcategui-Contreras, Antonio Guerra, Sebastian Niklitschek, Aldo Delgado,
• Abstract summary: We propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem.<n>Our method integrates a quantum marginal technique with convolutional denoising autoencoders.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a quantum marginal imposition technique with convolutional denoising autoencoders. The loss function is carefully designed to enforce essential physical constraints, including Hermiticity, positivity, and normalization. Through extensive numerical simulations, we demonstrate the effectiveness of our approach, achieving high success rates and accuracy. Furthermore, we show that, in many cases, our model offers a faster alternative to state-of-the-art semidefinite programming solvers without compromising solution quality. These results highlight the potential of machine learning techniques for solving complex problems in quantum mechanics.

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