Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure

• URL: http://arxiv.org/abs/2412.16480v1
• Date: Sat, 21 Dec 2024 04:20:44 GMT
• Title: Hybrid of Gradient Descent And Semidefinite Programming for Certifying Multipartite Entanglement Structure
• Authors: Kai Wu, Zhihua Chen, Zhen-Peng Xu, Zhihao Ma, Shao-Ming Fei,
• Abstract summary: Multipartite entanglement is a crucial resource for a wide range of quantum information processing tasks. We develop an efficient algorithm that combines semidefinite programming with a descent gradient method. Our method improves entanglement detection and provides deeper insights into the complex structures of many-body quantum systems.
• Score: 7.236334007028333
• License:
• Abstract: Multipartite entanglement is a crucial resource for a wide range of quantum information processing tasks, including quantum metrology, quantum computing, and quantum communication. The verification of multipartite entanglement, along with an understanding of its intrinsic structure, is of fundamental importance, both for the foundations of quantum mechanics and for the practical applications of quantum information technologies. Nonetheless, detecting entanglement structures remains a significant challenge, particularly for general states and large-scale quantum systems. To address this issue, we develop an efficient algorithm that combines semidefinite programming with a gradient descent method. This algorithm is designed to explore the entanglement structure by examining the inner polytope of the convex set that encompasses all states sharing the same entanglement properties. Through detailed examples, we demonstrate the superior performance of our approach compared to many of the best-known methods available today. Our method not only improves entanglement detection but also provides deeper insights into the complex structures of many-body quantum systems, which is essential for advancing quantum technologies

Related papers

• High-dimentional Multipartite Entanglement Structure Detection with Low Cost [18.876952671920133]
  We propose a neural network model to generate representations suitable for entanglement structure detection. Our method achieves over 95% detection accuracy for up to 19 qubits systems.
  arXiv  Detail & Related papers  (2024-08-23T12:09:26Z)
• Improved criteria of detecting multipartite entanglement structure [7.236334007028333]
  We propose a systematic method to construct powerful entanglement witnesses which identify better the multipartite entanglement structures. Our results may be applied to many quantum information processing tasks.
  arXiv  Detail & Related papers  (2024-06-11T14:01:22Z)
• Neural auto-designer for enhanced quantum kernels [59.616404192966016]
  We present a data-driven approach that automates the design of problem-specific quantum feature maps. Our work highlights the substantial role of deep learning in advancing quantum machine learning.
  arXiv  Detail & Related papers  (2024-01-20T03:11:59Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Entanglement-Assisted Quantum Networks: Mechanics, Enabling Technologies, Challenges, and Research Directions [66.27337498864556]
  This paper presents a comprehensive survey of entanglement-assisted quantum networks. It provides a detailed overview of the network structure, working principles, and development stages. It also emphasizes open research directions, including architecture design, entanglement-based network issues, and standardization.
  arXiv  Detail & Related papers  (2023-07-24T02:48:22Z)
• Modern applications of machine learning in quantum sciences [51.09906911582811]
  We cover the use of deep learning and kernel methods in supervised, unsupervised, and reinforcement learning algorithms. We discuss more specialized topics such as differentiable programming, generative models, statistical approach to machine learning, and quantum machine learning.
  arXiv  Detail & Related papers  (2022-04-08T17:48:59Z)
• Detecting entanglement in quantum many-body systems via permutation moments [4.376631240407246]
  We propose a framework for designing multipartite entanglement criteria based on permutation moments. These criteria show strong detection capability in the multi-qubit Ising model with a long-range $XY$ Hamiltonian. Our framework can also be generalized to detect the much more complicated entanglement structure in quantum many-body systems.
  arXiv  Detail & Related papers  (2022-03-16T04:39:54Z)
• Learning quantum phases via single-qubit disentanglement [4.266508670102269]
  We present a novel and efficient quantum phase transition, utilizing disentanglement with reinforcement learning-optimized variational quantum circuits. Our approach not only identifies phase transitions based on the performance of the disentangling circuits but also exhibits impressive scalability, facilitating its application in larger and more complex quantum systems.
  arXiv  Detail & Related papers  (2021-07-08T00:15:31Z)
• On exploring the potential of quantum auto-encoder for learning quantum systems [60.909817434753315]
  We devise three effective QAE-based learning protocols to address three classically computational hard learning problems. Our work sheds new light on developing advanced quantum learning algorithms to accomplish hard quantum physics and quantum information processing tasks.
  arXiv  Detail & Related papers  (2021-06-29T14:01:40Z)
• Quantum Geometric Machine Learning for Quantum Circuits and Control [78.50747042819503]
  We review and extend the application of deep learning to quantum geometric control problems. We demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
  arXiv  Detail & Related papers  (2020-06-19T19:12:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.