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Machine Learning Methods for Detecting and Quantifying Entanglement in Multipartite Qubit Systems

TOMMASO FALASCHI

Published Sep 26, 2026• 0 citations
OpenAlex

Abstract

Quantum entanglement is a fundamental resource in quantum information, but its characterization becomes increasingly challenging as the size of multipartite systems grows. This thesis investigates machine learning methods to detect and quantify entanglement in pure multiqubit states using only single qubit Pauli expectation values. Two complementary tasks are considered: the distinction between fully separable and entangled states, with particular attention to weakly entangled states close to the separability boundary, and the regression of normalized multipartite classical squashed entanglement. Several machine learning models are evaluated for detection, while multilayer perceptrons are employed for quantification. The low entanglement regime is investigated through dedicated datasets and targeted data augmentation strategies. The proposed approaches are studied for systems of 5, 10, 15, and 20 qubits and are further evaluated under realistic measurement conditions, including finite shot noise, asymmetric readout errors, calibration drift, and data acquired from real quantum processors. The study assesses the scalability, robustness, and practical limitations of data-driven entanglement characterization based on a linearly scaling set of local observables.

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Quantum entanglement is a fundamental resource in quantum information, but its characterization becomes increasingly challenging as the size of multipartite systems grows. This thesis investigates machine learning methods to detect and quantify entanglement in pure multiqubit states using only single qubit Pauli expectation values. Two complementary tasks are considered: the distinction between fully separable and entangled states, with particular attention to weakly entangled states close to the separability boundary, and the regression of normalized multipartite classical squashed entanglement. Several machine learning models are evaluated for detection, while multilayer perceptrons are employed for quantification. The low entanglement regime is investigated through dedicated datasets and targeted data augmentation strategies. The proposed approaches are studied for systems of 5, 10, 15, and 20 qubits and are further evaluated under realistic measurement conditions, including finite shot noise, asymmetric readout errors, calibration drift, and data acquired from real quantum processors. The study assesses the scalability, robustness, and practical limitations of data-driven entanglement characterization based on a linearly scaling set of local observables.
Entanglement plays a pivotal role in numerous quantum applications, and as technology progresses, entanglement systems continue to expand. However, quantifying entanglement is a complex problem, particularly for multipartite quantum states. The currently available entanglement measures suffer from high computational complexity, and for unknown multipartite entangled states, complete information about the quantum state is often necessary, further complicating calculations. In this paper, we train neural networks to quantify unknown multipartite entanglement using input features based on squared entanglement (SE) and outcome statistics data produced by locally measuring target quantum states. By leveraging machine learning techniques to handle non-linear relations between outcome statistics and entanglement measurement SE, we achieve high-precision quantification of unknown multipartite entanglement states with a linear number of measurements, avoiding the need for global measurements and quantum state tomography. The proposed method exhibits robustness against noise and extends its applicability to pure and mixed states, effectively scaling to large-scale multipartite entanglement systems. The results of the experiment show that the predicted entanglement measures are very close to the actual values, which confirms the effectiveness of the proposed method.
Detection of entanglement is an indispensable step to practical quantum computation and communication. Compared with the conventional entanglement witness method based on fidelity, we propose a flexible, machine learning assisted entanglement detection protocol that is robust to different types of noises and sample efficient. In this protocol, an entanglement classifier for a generic entangled state is obtained by training a classical machine learning model with a synthetic dataset. The dataset contains classical features of two types of states and their labels (either entangled or separable). The classical features of a state, which are expectation values of a set of k-local Pauli observables, are estimated sample-efficiently by the classical shadow method. In the numerical simulation, our classifier can detect the entanglement of 4-qubit GHZ states with coherent noise and W states mixed with large white noise, with high accuracy.
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.
We are entering a time in which quantum channel capacity is becoming increasingly dependent on having high-dimensional entangled systems. However, existing methods of detecting high-dimensional entanglement are hindered by their need for an unwieldy amount of measurements and computational power. Indeed, the use of entanglement witnesses circumvents this problem by only considering a small subset of the entangled states in Hilbert Space. Although efficient witnesses for 2-qubit Bell States and 3-Qubit GHZ states are well-known, the predominant “fidelity method" witnesses used for detecting multipartite W states remain relatively complex in the amount of measurements that they require. The work outlined in this thesis aims to improve on existing entanglement witnesses by drawing their correspondence with supervised learning techniques, specifically Support Vector Machines. In doing so, one can derive entanglement witnesses whose features (observables obtained via local operations and classical communications) can be ranked according to their impact on the classification of entangled and separable states. This method allows us to derive W state witnesses that require fewer measurements than those derived via the fidelity method. The process of Recursive Feature Elimination is also presented, by which we can define witnesses that can be decomposed into fewer Pauli observables at the cost of inferior tolerance to noise. Finally, we present the practical utility of our derived witnesses through physical experiments performed on the superconducting qubit devices provided by IBM.
This paper explores the use of machine learning techniques for detecting quantum entanglement in two-qubit systems. A dataset of randomly generated quantum states was constructed and labeled using the Positive Partial Transpose (PPT) criterion. Several supervised learning models, including Random Forest and Multi-Layer Perceptron neural networks, were trained to classify quantum states as entangled or separable. The results show that machine learning models can effectively learn patterns from quantum state data, while also highlighting the impact of dataset imbalance on classification performance. This study demonstrates the potential of machine learning as a complementary tool for quantum entanglement detection and provides insights into the challenges and opportunities of integrating artificial intelligence with quantum physics.
Quantum entanglement is a key resource in quantum computing and quantum information processing tasks. However, its quantification remains a major challenge since it cannot be directly extracted from physical observables. To address this issue, we study a few machine-learning based models to estimate the amount of entanglement in two-qubit as well as three-qubit systems. We use measurement outcomes as the input features and entanglement measures as the training labels. Our models predict entanglement without requiring the full state information. This demonstrates the potential of machine learning as an effcient and powerful tool for characterizing quantum entanglement