Quantum tomography by regularized linear regressions

Mu, Biqiang; Qi, Hongsheng; Petersen, Ian R.; Shi, Guodong

doi:10.1016/j.automatica.2020.108837

Cited by 14 publications

(6 citation statements)

References 27 publications

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“…The difference between θi,AWLS and θi,WLS is asymptotically small in comparison with θi,WLS [9]. Thus, the estimate ( 16) is accurate enough and asymptotically coincides with (8).…”

Section: Weighted Least Squares In Qdtmentioning

confidence: 84%

“…Remark 2: Ref. [9] has discussed regularized weighted regression in quantum state tomography. Their motivation is that the quantum state ρ is usually of low rank and thus it is reasonable to add a Tikhonov regularization as Sec.…”

Section: A Regularized Weighted Least Squaresmentioning

confidence: 99%

“…Quantum detector tomography (QDT), as the standard technique to characterize an unknown measurement process, is fundamental for device benchmarking and subsequent tasks such as quantum state tomography (QST) [7], [8], [9], quantum Hamiltonian identification [10], [11], [12], [13], [14], [15], quantum process tomography [16], [17], [18] and quantum control [19].…”

Section: Introductionmentioning

confidence: 99%

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On the regularization and optimization in quantum detector tomography

Xiao¹,

Wang²,

Zhang³

et al. 2022

Preprint

Self Cite

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Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are informationally complete or informationally incomplete. In the informationally complete scenario, without regularization, we optimize the resource (probe state) distribution by converting it to a semidefinite programming problem. Then in both the informationally complete and informationally incomplete scenarios, we discuss different regularization forms and prove

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“…The difference between θi,AWLS and θi,WLS is asymptotically small in comparison with θi,WLS [9]. Thus, the estimate ( 16) is accurate enough and asymptotically coincides with (8).…”

Section: Weighted Least Squares In Qdtmentioning

confidence: 84%

Section: A Regularized Weighted Least Squaresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the regularization and optimization in quantum detector tomography

Xiao¹,

Wang²,

Zhang³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In recent years, many quantum algorithms have erupted and showed their novelty and potential in solving NPhard problems, such as QAOA [13] and VQE [14]. Some effort on quantum computing has also focused on hard optimization problems [15][16][17][18]. Whereas, some non-von Neumann computers, such as general quantum computers and quantuminspired Ising machines, have shown quantum advantages in max-cut problems [13], protein folding problems [19] and so on.…”

Section: Introductionmentioning

confidence: 99%

Quantum-Inspired Solvers on Mixed-Integer Linear Programming Problem

Wang¹,

Cui²

2022

Preprint

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Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource consumption caused by complexity and failure of Moore's Law. Quantum-inspired Ising machines, as a new computing paradigm, can be used to solve integer programming problems by reducing them into Ising models. Therefore, it is necessary to understand the technical evolution of quantum inspired solvers to break the bottleneck. In this paper, the concept and traditional algorithms for MILP are introduced. Then, focused on Ising model, the principle and implementations of annealers and coherent Ising machines are summarized. Finally, the paper discusses the challenges and opportunities of miniaturized solvers in the future.

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“…(i) quantum state tomography (QST) which aims to estimate unknown states [4], [5], [6]; (ii) quantum process tomography which targets in identifying parameters of evolution operators [7], [8], [9], [10] (e.g., the system Hamiltonian [11], [12], [13], [14], [15], [16]); and (iii) quantum detector tomography (QDT) which aims to identify and calibrate quantum measurement devices.…”

Section: Introductionmentioning

confidence: 99%

Optimal and two-step adaptive quantum detector tomography

Xiao¹,

Wang²,

Dong³

et al. 2021

Preprint

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Quantum detector tomography is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we design optimal probe states for detector estimation based on the minimum upper bound of the mean squared error (UMSE) and the maximum robustness. We establish the minimum UMSE and the minimum condition number for quantum detectors and provide concrete examples that can achieve optimal detector tomography. In order to enhance estimation precision, we also propose a two-step adaptive detector tomography algorithm and investigate how this adaptive strategy can be used to achieve efficient estimation of quantum detectors. Moreover, the superposition of coherent states is used as probe states for quantum detector tomography and the estimation error is analyzed. Numerical results demonstrate the effectiveness of both the proposed optimal and adaptive quantum detector tomography methods.

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Quantum tomography by regularized linear regressions

Cited by 14 publications

References 27 publications

On the regularization and optimization in quantum detector tomography

On the regularization and optimization in quantum detector tomography

Quantum-Inspired Solvers on Mixed-Integer Linear Programming Problem

Optimal and two-step adaptive quantum detector tomography

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