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Shuixin Xiao1,2,Yuanlong Wang3,et al.[en_title][J].Control Theory and Technology,2024,22(2):222~234.[Copy]
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Quantum state tomography from observable time traces in closed quantum systems
ShuixinXiao1,2,YuanlongWang3,QiYu4,JunZhang1,DaoyiDong2,5,IanR.Petersen2
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(1 University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China 2 School of Engineering, The Australian National University, Canberra, ACT 2601, Australia;3 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4 Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, QLD 4111, Australia;5 School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia)
摘要:
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 O (1/N), 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 d ? 1 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
DOI:https://doi.org/10.1007/s11768-024-00215-9
基金项目:This work was supported by the National Natural Science Foundation of China (Nos. 62173229, 12288201), the Australian Research Council Future Fellowship Funding Scheme under Project FT220100656 and the Discovery Project Funding Scheme under Project DP210101938.
Quantum state tomography from observable time traces in closed quantum systems
Shuixin Xiao1,2,Yuanlong Wang3,Qi Yu4,Jun Zhang1,Daoyi Dong2,5,Ian R. Petersen2
(1 University of Michigan–Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China 2 School of Engineering, The Australian National University, Canberra, ACT 2601, Australia;3 Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;4 Centre for Quantum Computation and Communication Technology (Australian Research Council), Centre for Quantum Dynamics, Griffith University, Brisbane, QLD 4111, Australia;5 School of Engineering and Technology, University of New South Wales, Canberra, ACT 2600, Australia)
Abstract:
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 O (1/N), 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 d ? 1 observables, where d is the dimension of the quantum state, for informational completeness. Numerical examples demonstrate the effectiveness of our method.
Key words:  Quantum state tomography · Time trace · Quantum system identification