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quantum state tomography from observable time traces in closed quantum systems

Control Theory and Technology 2024年第2期22卷 222-234页

作者： Shuixin Xiao Yuanlong Wang Qi Yu Jun Zhang Daoyi Dong Ian R.Petersen University of Michigan–Shanghai Jiao Tong University Joint Institute Shanghai Jiao Tong UniversityShanghai200240China School of Engineering The Australian National UniversityCanberraACT2601Australia Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China Centre for quantum Computation and Communication Technology(Australian Research Council) Centre for Quantum DynamicsGriffith UniversityBrisbaneQLD4111Australia School of Engineering and Technology University of New South WalesCanberraACT2600Australia

The task to estimate all the parameters of an unknown quantum state, also called quantum state tomography, is essential for characterizing and controlling quantum systems. In this paper, we utilize observable time traces to identify the initial quantum state of a closed quantum system, based on the state space approach in the control theory. In the informationally complete scenario, we show that with a linear regression estimation (LRE), the mean squared error (MSE) scales as , where N is the resource number. In the informationally incomplete scenario, we introduce regularization LRE to perform the state tomography task. We employ PBH test to demonstrate that closed quantum systems with only one observable are informationally incomplete and propose using observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.

关键词： quantum state tomography Time trace quantum system identification

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Optical neural network quantum state tomography

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Advanced Photonics 2022年第2期4卷 91-97页

作者： Ying Zuo Chenfeng Cao Ningping Cao Xuanying Lai Bei Zeng Shengwang Du The Hong Kong University of Science and Technology Department of PhysicsHong KongChina University of Guelph Department of Mathematics and StatisticsGuelphOntarioCanada University of Waterloo Institute for Quantum ComputingWaterlooOntarioCanada The University of Texas at Dallas Department of PhysicsRichardsonTexasUnited States

quantum state tomography(QST)is a crucial ingredient for almost all aspects of experimental quantum information processing.As an analog of the“imaging”technique in quantum settings,QST is born to be a data science problem,where machine learning techniques,noticeably neural networks,have been applied extensively.We build and demonstrate an optical neural network(ONN)for photonic polarization qubit QST.The ONN is equipped with built-in optical nonlinear activation functions based on electromagnetically induced transparency.The experimental results show that our ONN can determine the phase parameter of the qubit state accurately.As optics are highly desired for quantum interconnections,our ONN-QST may contribute to the realization of optical quantum networks and inspire the ideas combining artificial optical intelligence with quantum information studies.

关键词： optical neural network quantum state tomography quantum optics

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Machine Learning for Data Reduction in quantum state tomography

Machine Learning for Data Reduction in Quantum State Tomogra...

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第37届中国控制会议

作者： Ximin Liu Sicong Lu Rebing Wu Institute of Microelectronics Tsinghua University Department of Automation Tsinghua University

The purpose of quantum state tomography（QST） is to obtain a complete quantum state by reconstructing a density matrix from experimental data and therefore gives researchers a powerful tool to analyze complex synthetic quantum systems.In the past decades,many methods have been developed to improve the efficiency of quantum state tomography（QST）,such as old methods: compress sensing on almost pure state and low-rank systems,new method: using restricted Boltzmann machine on systems of quantum many-body.However,they are both limited to some certain systems.In this paper,we introduce an universal method using deep neural networks based on stacked denoising autoencoder,which probably can help finish QST on all types of systems with a much smaller number of measurements and therefore is very efficient.

关键词： quantum state tomography deep neural networks stacked denoising autoencoder

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Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state

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Chinese Physics B 2022年第5期31卷 101-106页

作者：刘晓芳李冬芬郑云丹杨小龙周杰谭玉乔刘明哲 School of Computer and Network Security Chengdu University of TechnologyChengdu 610059China

quantum controlled teleportation is the transmission of the quantum state under the supervision of a third party.This paper presents the theoretical and experimental results of an arbitrary two-qubit quantum controlled teleportation scheme,in which the sender Alice only needs to perform two Bell state measurements and the receiver Bob can perform an appropriate unitary operation to reconstruct the arbitrary two-qubit states under the control of the supervisor Charlie.The operation process of the scheme is verified on the IBM quantum experience platform,and the accuracy of the transmitted quantum state is further checked by performing quantum state tomography.Meanwhile,a good fidelity is obtained by using the theoretical density matrix and the experimental density matrix.A sequence of photonic states is introduced to analyze the possible intercept-replace-resend,intercept-measure-resend,and entanglement-measure-resend attacks on this scheme.The results proved that our scheme is highly secure.

关键词： IBM quantum experience controlled quantum teleportation fidelity quantum state tomography

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Quantifying entanglement of two-qubit Werner states

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Communications in Theoretical Physics 2021年第8期73卷 75-81页

作者： Artur Czerwinski Institute of Physics Faculty of PhysicsAstronomy and InformaticsNicolaus Copernicus UniversityGrudziadzka 587-100 TorunPoland

In this article,we introduce a framework for entanglement quantification of photon pairs represented by two-qubit Werner states.The measurement scheme is based on the symmetric informationally complete POVM.To make the framework realistic,we impose the Poisson noise on the measured two-photon coincidences.For various settings,numerical simulations were performed to evaluate the efficiency of the framework.

关键词： Werner states quantum state tomography entanglement characterization concurrence

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