Machine Learning approach to reconstruct Density Matrices from Quantum Marginals

TL;DR

This paper introduces a machine learning method combining autoencoders and physical constraints to efficiently reconstruct global quantum density matrices from given marginals, outperforming traditional optimization techniques in speed and accuracy.

Contribution

It presents a novel ML-based framework that integrates quantum marginal constraints with autoencoders, offering a faster alternative to existing semidefinite programming methods for density matrix reconstruction.

Findings

High success rates in numerical simulations

Faster than state-of-the-art solvers

Maintains high accuracy and physical validity

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.