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Data-Driven Quantification of Quantum k-Entanglement via Machine Learning
Jie Guo1, Jinchuan Hou1, Xiaofei Qi2,3
1College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, China.
Entropy (Basel, Switzerland)
|July 28, 2026
Summary
We developed a machine learning framework to quickly approximate k-entanglement measures, a key quantum resource. This approach significantly speeds up calculations for quantum information processing and simulation tasks.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Quantum Physics
Background:
- * k-entanglement is a crucial quantum resource for multipartite quantum systems.
- * Identifying and quantifying k-entanglement is vital for quantum information processing, simulation, and metrology.
- * Current methods for calculating k-entanglement measures are computationally intensive due to high-dimensional optimization.
Purpose of the Study:
- * To propose a machine learning-based surrogate framework for approximating the witness-based k-entanglement measure Ew(k,n).
- * To reformulate the numerical evaluation of E˜w(k,n)(ρ) as a supervised regression problem.
- * To significantly reduce computational time for k-entanglement measure approximation.
Main Methods:
- * A supervised regression approach using density matrices as input and finite witness databases for labels.
- * A stacking ensemble combining multilayer perceptrons (MLPs), convolutional neural networks (CNNs), and LightGBM.
- * Numerical experiments on 3- and 4-qubit systems, including Werner states and noisy circuit-generated states.
Main Results:
- * The learned models achieved high predictive accuracy (MAE, MSE, R2).
- * The framework provides millisecond-level inference for single-state evaluation.
- * Significant reduction in computational time compared to optimization-based methods while maintaining accuracy.
Conclusions:
- * The proposed framework offers an efficient numerical surrogate for rapid approximation of witness-based k-entanglement measures.
- * The machine learning approach demonstrates potential for practical applications in quantum information.
- * Further validation is needed for larger systems and experimental data.
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