Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in high-dimensional systems. We present a machine learning approach based on support vector regression (SVR) that directly estimates the coherence measures and the geometric measure of quantum entanglement using minimal experimental resources. Our method requires only the diagonal entries of the density matrix, along with the traces of the squared and cubed density matrices for quantum coherence, and additionally along with the traces of the squared and cubed reduced density matrix for estimating quantum entanglement. These quantities can be obtained through random measurements or a hybrid quantum-classical framework. This approach significantly reduces the resource overhead compared to quantum state tomography while maintaining high accuracy. {Furthermore, the support vector quantile regression (SVQR) with pinball loss is employed to prevent SVR overestimation. This model not only ensures that over 95\% of predictions are conservative lower bounds in most cases, but also maintains this lower-bound reliability for over 93\% of predictions, despite 2\% perturbations in the input features.} The proposed technique provides a practical and scalable tool for characterizing quantum resources across computation, communication, and metrology applications.
Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in high-dimensional systems. We present a machine learning approach based on support vector regression (SVR) that directly estimates the coherence measures and the geometric measure of quantum entanglement using minimal experimental resources. Our method requires only the diagonal entries of the density matrix, along with the traces of the squared and cubed density matrices for quantum coherence, and additionally along with the traces of the squared and cubed reduced density matrix for estimating quantum entanglement. These quantities can be obtained through random measurements or a hybrid quantum-classical framework. This approach significantly reduces the resource overhead compared to quantum state tomography while maintaining high accuracy. {Furthermore, the support vector quantile regression (SVQR) with pinball loss is employed to prevent SVR overestimation. This model not only ensures that over 95% of predictions are conservative lower bounds in most cases, but also maintains this lower-bound reliability for over 93% of predictions, despite 2% perturbations in the input features.} The proposed technique provides a practical and scalable tool for characterizing quantum resources across computation, communication, and metrology applications.
Abstract Quantum measurements are inherently noisy and data-intensive, posing significant challenges for reliable entanglement detection and the scalability of quantum technologies. While error mitigation techniques exist, they often require a prohibitive number of measurements, making the process resource-intensive. In this work, we demonstrate that by explicitly accounting for measurement errors, high-fidelity entanglement detection can be achieved with significantly less data.We introduce a machine-learning-based approach that delivers noise-resilient entanglement classification even with imperfect measurements. Our method employs support vector machines (SVMs) trained on features from Pauli measurements to construct a robust optimal entanglement witness (ROEW). By optimizing SVM parameters against worst-case errors, our protocol ensures effectiveness under unknown measurement noise. Numerical experiments show that ROEW maintains high classification accuracy even when measurement errors exceed 10\%. Crucially, we demonstrate that training the model using only 20\% of the typical dataset suffices to achieve high accuracy and substantial error reduction. Our proposed ROEW significantly outperforms traditional non-robust models, maintaining superior detection performance under elevated noise. This work bridges machine learning and quantum information science, offering a practical tool for noise-robust quantum characterization and advancing the feasibility of entanglement-based technologies.
In this work, we investigate the application of Machine Learning (ML) algorithms to the identification and quantitative characterization of quantum entanglement in polarization-entangled photon pairs. The analysis is based on simulated symmetric, informationally complete, positive operator-valued measure (SIC-POVM) measurement data, where each two-qubit state is represented by a 16-dimensional measurement vector corresponding to experimentally accessible coincidence counts. The generated SIC-POVM measurement data include Poissonian shot noise. Several supervised ML algorithms, including Logistic Regression, k-Nearest Neighbors, Decision Trees, Support Vector Machines, and Random Forests, are applied to the classification of separable and entangled states directly from raw measurement data, without explicit density matrix reconstruction or the use of conventional separability criteria. The study additionally explores clustering methods and nonlinear regression techniques for estimating continuous entanglement measures. The obtained results demonstrate that ML methods can achieve very high classification accuracy, even under extremely limited training conditions. These findings indicate that ML may provide an efficient alternative to conventional quantum-state analysis under simulated Poissonian noise conditions.
k-entanglement, including entanglement relative to full separability and genuinely multipartite entanglement, is a fundamental quantum resource in multipartite quantum systems. Its identification and quantification play essential roles in quantum information processing, quantum simulation, and quantum metrology. However, the practical computation of rigorous k-entanglement measures remains highly challenging due to the need for high-dimensional optimization. In this work, we propose a machine-learning-based surrogate framework for approximating the witness-based k-entanglement measure Ew(k,n). The numerical evaluation of the computationally realized quantity E˜w(k,n)(ρ) is reformulated as a supervised regression problem, where the input is the density matrix ρ and the labels are obtained from finite witness databases. The framework combines multilayer perceptrons (MLPs), convolutional neural networks (CNNs), and light gradient boosting machine (LightGBM) through a stacking ensemble. Numerical experiments are performed for 3- and 4-qubit systems as representative demonstrations of the proposed workflow. The results show that the learned models achieve high predictive accuracy in terms of MAE, MSE, and R2, while providing millisecond-level inference for single-state evaluation. Werner state tests serve as symmetric benchmark checks, and an additional four-qubit noisy circuit-generated state family, obtained from finite-depth circuit preparation followed by local amplitude-damping noise, is used as a structured physical test beyond random density matrices. Compared with the optimization-based evaluation, the trained surrogate model significantly reduces the computational time while maintaining accuracy within the tested system sizes and data distributions. These results show that the proposed framework provides an efficient numerical surrogate for rapid approximation of witness-based k-entanglement measures, while extensions to larger systems and experimental data require further validation.
Quantum Fisher information (QFI) is a fundamental quantifier in quantum metrology, determining the ultimate precision achievable in parameter-estimation protocols through the quantum Cramér-Rao bound. However, direct evaluation of the QFI generally requires detailed knowledge of the density matrix, making it increasingly demanding as the Hilbert-space dimension grows. In this work, we investigate the extent to which the QFI of multipartite quantum systems can be predicted from a limited set of experimentally accessible quantities using support vector regression (SVR). By comparing different physically motivated features, we identify a dominant feature set governing QFI and show that the predictive power of collective spin moments alone decreases as system size and consequently Hilbert-space dimension grows. We demonstrate that QFI is governed primarily by the interplay between collective covariance and low-order spectral moments of the density matrix. Our results identify the physically relevant information sectors governing the QFI and demonstrate that accurate estimation of metrological sensitivity can be achieved from a restricted set of experimentally accessible quantities without requiring full quantum-state tomography.
Quantum entanglement is a powerful resource for quantum-enhanced technologies. However, its reliable quantification remains challenging due to the exponential scaling of the Hilbert space with system size, which renders full state tomography infeasible. Moreover, experimentally estimating entanglement typically requires a large number of measurement samples leading to a significant overhead. In this work, we present two models, a feed-forward neural network and an attention-based model, to accurately predict the bipartite second Renyi from projective measurements of quantum states. We benchmark their performance against standard classical shadow estimators and find that the machine-learning approaches achieve higher accuracy and improved sample efficiency across a range of system sizes. Our results demonstrate the potential of machine learning for scalable and efficient estimation of quantum correlations.
Abstract Quantifying entanglement measures for quantum states with unknown density matrices is a challenging task. Machine learning offers a new perspective to address this problem. By training machine learning models using experimentally measurable data, we can predict the target entanglement measures. In this study, we compare various machine learning models and find that the linear regression and stack models perform better than others. We investigate the model’s impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better results. Additionally, we investigate which measurable data has better predictive power for target entanglement measures. Using correlation analysis and principal component analysis, we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.