{"title":"Fast and noise-robust quantum state tomography based on ELM","authors":"Xiao-Dong Wu, Shuang Cong","doi":"10.1142/s0219749923500521","DOIUrl":null,"url":null,"abstract":"<p>This paper proposed a quantum state tomography approach based on the extreme learning machine (ELM), which is available in the reconstruction of quantum states via a lightweight neural network. The key step of the proposed tomography approach is to employ the ELM to approximate the complex mapping between the measurement values sequence and the real density matrix. After obtaining the output of the ELM-based estimator, a matrix transformation technique is used to make the network outputs satisfy quantum state constraints. Compared with deep learning-based tomography approaches, our proposed ELM-based approach enables both high-fidelity and high-efficiency quantum state tomography with only one training process under the condition of very few numbers of training samples, network layers and hidden layer nodes. In addition, the proposed tomography approach is robust to noisy measurement values, since the ELM-based estimator is quite lightweight. Simulations on the tomography of eigenstates, superposition states and mixed states are presented to verify our theoretical findings. Also, the superiority of the ELM-based tomography approach is demonstrated in comparison with that based on the radial basis function network, convolutional neural network and maximum likelihood estimation approach.</p>","PeriodicalId":51058,"journal":{"name":"International Journal of Quantum Information","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Quantum Information","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1142/s0219749923500521","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper proposed a quantum state tomography approach based on the extreme learning machine (ELM), which is available in the reconstruction of quantum states via a lightweight neural network. The key step of the proposed tomography approach is to employ the ELM to approximate the complex mapping between the measurement values sequence and the real density matrix. After obtaining the output of the ELM-based estimator, a matrix transformation technique is used to make the network outputs satisfy quantum state constraints. Compared with deep learning-based tomography approaches, our proposed ELM-based approach enables both high-fidelity and high-efficiency quantum state tomography with only one training process under the condition of very few numbers of training samples, network layers and hidden layer nodes. In addition, the proposed tomography approach is robust to noisy measurement values, since the ELM-based estimator is quite lightweight. Simulations on the tomography of eigenstates, superposition states and mixed states are presented to verify our theoretical findings. Also, the superiority of the ELM-based tomography approach is demonstrated in comparison with that based on the radial basis function network, convolutional neural network and maximum likelihood estimation approach.
本文提出了一种基于极端学习机(ELM)的量子态层析方法,可通过轻量级神经网络重建量子态。该方法的关键步骤是利用 ELM 逼近测量值序列与真实密度矩阵之间的复杂映射。在获得基于 ELM 的估计器输出后,利用矩阵变换技术使网络输出满足量子态约束。与基于深度学习的层析成像方法相比,我们提出的基于 ELM 的方法在训练样本、网络层和隐藏层节点数量极少的条件下,只需一次训练过程就能实现高保真和高效率的量子态层析成像。此外,由于基于 ELM 的估计器非常轻便,因此所提出的层析方法对噪声测量值具有鲁棒性。为了验证我们的理论发现,我们对特征状态、叠加状态和混合状态进行了层析成像模拟。此外,与基于径向基函数网络、卷积神经网络和最大似然估计方法的层析成像方法相比,基于 ELM 的层析成像方法更具优势。
期刊介绍:
The International Journal of Quantum Information (IJQI) provides a forum for the interdisciplinary field of Quantum Information Science. In particular, we welcome contributions in these areas of experimental and theoretical research:
Quantum Cryptography
Quantum Computation
Quantum Communication
Fundamentals of Quantum Mechanics
Authors are welcome to submit quality research and review papers as well as short correspondences in both theoretical and experimental areas. Submitted articles will be refereed prior to acceptance for publication in the Journal.