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arXiv:2211.05592

Towards efficient and generic entanglement detection by machine learning

Jue Xu, Qi Zhao

Published Nov 10, 2022• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2211.05592

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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.
This paper introduces a new method to identify quantum entanglement in diverse quantum states by leveraging artificial intelligence. We establish a robust classifier by training a machine learning model on a synthetically generated dataset, enabling accurate differentiation of entangled states even amidst significant noise. The technique employs classical features derived from quantum state measurements, optimizing for sample efficiency. Numerical evaluations demonstrate this approach achieves high accuracy in classifying entangled multi-qubit states under various noisy environments.
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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.
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.
Abstract Quantum properties, such as entanglement and coherence, are indispensable resources in various quantum information processing tasks. However, there still lacks an efficient and scalable way to detecting these useful features especially for high-dimensional and multipartite quantum systems. In this work, we exploit the convexity of samples without the desired quantum features and design an unsupervised machine learning method to detect the presence of such features as anomalies. Particularly, in the context of entanglement detection, we propose a complex-valued neural network composed of pseudo-siamese network and generative adversarial net, and then train it with only separable states to construct non-linear witnesses for entanglement. It is shown via numerical examples, ranging from two-qubit to ten-qubit systems, that our network is able to achieve high detection accuracy which is above 97.5% on average. Moreover, it is capable of revealing rich structures of entanglement, such as partial entanglement among subsystems. Our results are readily applicable to the detection of other quantum resources such as Bell nonlocality and steerability, and thus our work could provide a powerful tool to extract quantum features hidden in multipartite quantum data.
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.