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arXiv:2401.12041 · Quantum Information Processing

Trade-off between bagging and boosting for quantum separability-entanglement classification

Sanuja D. Mohanty, Ram Narayan Patro, Pradyut Kumar Biswal, Biswajit Pradhan, Sk Sazim

Published Jul 15, 2024• 1 citation
arXivHTMLPDF

Abstract

Abstract Certifying whether an arbitrary quantum system is entangled or not, is, in general, an NP-hard problem. Though various necessary and sufficient conditions have already been explored in this regard for lower-dimensional systems, it is hard to extend them to higher dimensions. Recently, an ensemble bagging and convex hull approximation (CHA) approach (together, BCHA) was proposed and it strongly suggests employing a machine learning technique for the separability-entanglement classification problem. However, BCHA does only incorporate the balanced dataset for classification tasks which results in lower average accuracy. In order to solve the data imbalance problem in the present literature, an exploration of the boosting technique has been carried out, and a trade-off between the boosting and bagging-based ensemble classifier is explored for quantum separability problems. For the two-qubit and two-qutrit quantum systems, the pros and cons of the proposed random under-sampling boost CHA (RUSBCHA) for the quantum separability problem are compared with the state-of-the-art CHA and BCHA approaches. As the data are highly unbalanced, performance measures such as overall accuracy, average accuracy, F-measure, and G-mean are evaluated for a fair comparison. The outcomes suggest that RUSBCHA is an alternative to the BCHA approach. Also, for several cases, performance improvements are observed for RUSBCHA since the data are imbalanced.

DOI
10.1007/s11128-024-04469-9

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The problem of determining whether a given quantum state is entangled lies at the heart of quantum information processing. Despite the many methods---such as the positive partial transpose criterion and the kkk-symmetric extendibility criterion---to tackle this problem, none of them enables a general, practical solution due to the problem's NP-hard complexity. Explicitly, separable states form a high-dimensional convex set of vastly complicated structures. In this work, we build a different separability-entanglement classifier underpinned by machine learning techniques. We use standard tools from machine learning to learn the entanglement feature of arbitrary given quantum states. We perform substantial numerical tests on two-qubit and two-qutrit systems, and the results indicate that our method can outperform the existing methods in generic cases in terms of both speed and accuracy. This opens up avenues to explore quantum entanglement via the machine learning approach.
Quantum entanglement becomes more complicated and capricious when more than two parties are involved. There have been methods for classifying some inequivalent multipartite entanglements, such as GHZ states and W states. In this paper, based on the fact that the set of all W states is convex, we approximate the convex hull by some critical points from the inside and propose a method of classification via the tangent hyperplane. To accelerate the calculation, we bring ensemble learning of machine learning into the algorithm, thus improving the accuracy of the classification.
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.
Abstract Quantum machine learning integrates quantum computing with classical machine learning techniques to enhance computational power and efficiency. A major challenge in Quantum machine learning is developing robust quantum classifiers capable of accurately processing and classifying complex datasets. In this work, we present an advanced approach leveraging data re-uploading, a strategy that cyclically encodes classical data into quantum states to improve classifier performance. We examine two cost functions—fidelity and trace distance—across various quantum classifier configurations, including single-qubit, two-qubit, and entangled two-qubit systems. Additionally, we evaluate four optimization techniques (L-BFGS-B, COBYLA, Nelder-Mead, and SLSQP) to determine their effectiveness in optimizing quantum circuits for both linear and non-linear classification tasks. Our results show that the choice of optimization method significantly impacts classifier performance, with L-BFGS-B and COBYLA often yielding superior accuracy. The two-qubit entangled classifier shows improved accuracy over its non-entangled counterpart, albeit with increased computational cost. Also, the two-qubit entangled classifier are the best option for real word random dataset in order to accuracy and computational cost. Linear classification tasks generally exhibit more stable performance across optimization techniques compared to non-linear tasks. Our findings highlight the potential of data re-uploading in Quantum machine learning outperforming existing quantum classifier models in terms of accuracy and robustness. This work contributes to the growing field of Quantum machine learning by providing a comprehensive comparison of classification strategies and optimization techniques in quantum computing environments, offering a foundation for developing more efficient and accurate quantum classifiers.
Quantum entanglement is a unique correlation phenomenon in quantum mechanics, and the measurement of quantum entanglement plays an important role in quantum computing and quantum communication. Many mainstream entanglement criteria and measurement methods currently known have shortcomings in certain aspects, such as not being sufficient or necessary conditions for entanglement, or only being effective in simple cases such as 2-qubits or pure states. In this work, we will propose a scheme for measuring quantum entanglement, which starts with treating the set of quantum separable states as a convex hull of quantum separable pure states, and analyzes the properties of the convex hull to obtain a new form of entanglement measurement. Although a large amount of data is required in the measurement process, this method is not only applicable to 2-qubit quantum states, but also a entanglement measurement method that can be applied to any dimension and any fragment. We will provide several examples to compare their results with other entanglement metrics and entanglement determination methods to verify their feasibility.
Quantum annealing has been widely used to optimize machine learning such as ensemble classifiers. This ensemble classifier enhances classification performance through the combination of multiple accurate and diverse base classifiers. It benefits from the “perturb and combine” strategy which involves using the random subspace as the prevalent approach to perturb input data. There are several methods to generate a random subspace which include bagging, boosting, clustering, and, more recently, clustering balancing. The main contribution of this research was to improve the accuracy of the ensemble classifier using the hybrid quantum annealing method. The process involved making larger, stronger, and more balanced clusters through 1) the modification of the range of values from K in incremental clustering, 2) the adjustment of the clusters to be stronger and more balanced, and 3) the optimization of pure-class clusters using quantum annealing. The proposed method was tested and evaluated on 10 benchmark datasets from the UCI repository and the results were compared with current approaches. The results showed that the proposed method has better accuracy than the others due to the larger, stronger, and more balanced clusters generated as well as the better trade-off between accuracy and diversity.