Quantum tomography by regularized linear regressions
Mu, Biqiang1; Qi, Hongsheng1,2; Petersen, Ian R.3; Shi, Guodong4
Source PublicationAUTOMATICA
AbstractIn this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields random outcomes, from which a classical linear regression model can be established. First of all, for complete or over-complete measurement bases, we show that the empirical data can be utilized for the construction of a weighted least squares estimate (LSE) for quantum tomography. Taking into consideration the trace-one condition, a constrained weighted LSE can be explicitly computed, being the optimal unbiased estimation among all linear estimators. Next, for general measurement bases, we show that l(2)-regularization with proper regularization gain provides even a lower mean-square error under a cost in bias. The optimal regularization parameter is defined in terms of a risk characterization for any finite sample size and a resulting implementable estimator is proposed. Finally, a concise and unified formula is established for the regularization parameter with complete measurement basis under an equivalent regression model, which proves that the proposed implementable tuning estimator is asymptotically optimal as the number of copies grows to infinity. Additionally, several numerical examples are provided to validate the established results. (C) 2020 Elsevier Ltd. All rights reserved.
KeywordQuantum state tomography Linear regression Regularization
Indexed BySCI
Funding ProjectNational Key R&D Program of China[2018YFA0703800] ; National Natural Science Foundation of China[61873262] ; Australian Research Council[DP180101805] ; Australian Research Council[DP190103615]
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000519656500014
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Document Type期刊论文
Corresponding AuthorQi, Hongsheng
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Australian Natl Univ, Res Sch Elect Energy & Mat Engn, Canberra, ACT 0200, Australia
4.Univ Sydney, Australian Ctr Field Robot, Sch Aerosp Mech & Mechatron Engn, Sydney, NSW 2006, Australia
Recommended Citation
GB/T 7714
Mu, Biqiang,Qi, Hongsheng,Petersen, Ian R.,et al. Quantum tomography by regularized linear regressions[J]. AUTOMATICA,2020,114:15.
APA Mu, Biqiang,Qi, Hongsheng,Petersen, Ian R.,&Shi, Guodong.(2020).Quantum tomography by regularized linear regressions.AUTOMATICA,114,15.
MLA Mu, Biqiang,et al."Quantum tomography by regularized linear regressions".AUTOMATICA 114(2020):15.
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