Reliable quantification of quantum entanglement in high-spin or many body systems remains a major computational challenge. Extending machine learning techniques to genuinely high dimensional settings is urgently needed. In this study, we investigate ensemble machine learning as a scalable framework for estimating entanglement, quantified by the negativity, in high-spin quantum systems. We construct a stacked ensemble regressor integrating Neural Networks, XGBoost, and Extra Trees. The model is trained on real-coefficient pure states and mixed Werner states for [Formula: see text], and 5, corresponding to the orthogonal ensemble characteristic of time-reversal-symmetric systems. With CatBoost serving as the meta-learner, the ensemble achieves consistently high predictive accuracy. Statistical validation across five independent random seeds confirms negligible run-to-run variance in all reported metrics. Residual analysis reveals a heteroscedastic error structure: prediction fidelity is highest near [Formula: see text] and [Formula: see text], with peak variance in the intermediate regime ([Formula: see text]-0.7). Empirical scaling laws for training time and memory consumption are derived, showing that the [Formula: see text] growth of the Werner-state feature space poses a scalability ceiling for raw density-matrix representations beyond [Formula: see text]. Moreover, we derive an empirical formula linking the required dataset size to system dimensionality and desired prediction accuracy. Our findings demonstrate that ensemble learning provides a robust and trustworthy tool for characterizing entanglement in high dimensional quantum physics.
Reliable quantification of quantum entanglement in high-spin or many body systems remains a major computational challenge. Extending machine learning techniques to genuinely high dimensional settings is urgently needed. In this study, we investigate ensemble machine learning as a scalable framework for estimating entanglement, quantified by the negativity, in high-spin quantum systems. We construct a stacked ensemble regressor integrating Neural Networks, XGBoost, and Extra Trees. The model is trained on real-coefficient pure states and mixed Werner states for [Formula: see text], and 5, corresponding to the orthogonal ensemble characteristic of time-reversal-symmetric systems. With CatBoost serving as the meta-learner, the ensemble achieves consistently high predictive accuracy. Statistical validation across five independent random seeds confirms negligible run-to-run variance in all reported metrics. Residual analysis reveals a heteroscedastic error structure: prediction fidelity is highest near [Formula: see text] and [Formula: see text], with peak variance in the intermediate regime ([Formula: see text]-0.7). Empirical scaling laws for training time and memory consumption are derived, showing that the [Formula: see text] growth of the Werner-state feature space poses a scalability ceiling for raw density-matrix representations beyond [Formula: see text]. Moreover, we derive an empirical formula linking the required dataset size to system dimensionality and desired prediction accuracy. Our findings demonstrate that ensemble learning provides a robust and trustworthy tool for characterizing entanglement in high dimensional quantum physics.
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.
Abstract Entanglement detection, the process of verifying quantum entanglement is a fundamental challenge in quantum information processing. Various approaches have been proposed to address this challenge, with many recent studies applying supervised machine learning methods. While these methods have demonstrated high accuracy in entanglement detection, it is reasonable to assume that the entangled states themselves are not definitively known. To address this limitation, we have devised a machine learning method for entanglement detection based on positive-unlabeled learning, a classical machine learning framework that does not use label information from negative data. Using a deep neural network model to synthetic dataset under the assumption of mixed states, we conducted experiments on a classical computer to valid the effectiveness and characteristics of the proposed method. Our approach introduces a novel framework that accounts for the data generation constraints in the training process of entanglement detector, thereby advancing machine learning techniques in quantum information science.
A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that make them up but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log(B) operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains computationally challenging for multiqubit systems due to exponential scaling. We present a machine learning framework that efficiently predicts the quantum W-distance by extracting physically meaningful features from quantum state pairs, including Pauli measurements, statistical moments, quantum fidelity, and entanglement measures. Our approach employs both classical neural networks and traditional machine learning models. On three-qubit systems, the best-performing Random Forest model achieves near-perfect accuracy (R2=0.9999) with mean absolute errors on the order of 10−5. We further validate the framework's practical utility by successfully verifying two fundamental theoretical propositions in quantum information theory: the bound on measurement probability differences between unitary operations and the W1 gate error rate bound. The results establish machine learning as a viable and scalable alternative to traditional numerical methods for W-distance computation, with particular promise for real-time quantum circuit assessment and error correction protocol design in NISQ devices.
Abstract With the rapid growth of controllable qubits in recent years, experimental multipartite entangled states can be created with high fidelity in various moderate‐ and large‐scale physical systems. However, the characterization of multipartite entanglement structure remains a formidable challenge, as traditionally it requires exponential number of local measurements to realize the identification. Machine learning is demonstrated to be an efficient tool to detect the underlying entanglement structure for ideal states, but it has non‐negligible underperformance when tackling imperfect experimental data in reality. Here, a modified classifier based on feed‐forward neural network to predict experimental entanglement structure in terms of entanglement intactness and depth is proposed. By preprocessing the input data, the classifier maintains efficiency and reliability against experimental noises, with the accuracy being enhanced from 69.7% to 91.2% for 6‐qubit entangled states in spin systems. This method is anticipated to shed light on future studies of entanglement structure, in particular when the number of controlled qubits reaches explosive growth in practice.