Self-guided quantum state tomography for limited resources

Ahmad, Syed Tihaam; Farooq, Ahmad; Shin, Hyundong

doi:10.1038/s41598-022-09143-7

Cited by 7 publications

(5 citation statements)

References 29 publications

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“…Other approaches do not make any assumption on ρ. In 2014 Self-Guided Quantum Tomography (SGQT) was introduced [9] and further studied in [10], [11]. It makes no assumption on ρ, and the number of measurements scales reasonably with the number of qubits.…”

Section: Prior Work and Problem Statementmentioning

confidence: 99%

Pure state tomography with parallel unentangled measurements

Verdeil¹,

Deville²

2022

Preprint

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Section: Prior Work and Problem Statementmentioning

confidence: 99%

Pure state tomography with parallel unentangled measurements

Verdeil¹,

Deville²

2022

Preprint

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“…Moreover, experimental realization of adaptive tomography has been demonstrated in [29]. Following this, a self-guided adaptive quantum tomography has been studied in [30].…”

Section: Introductionmentioning

confidence: 97%

A Bayesian quantum state tomography along with adaptive frameworks based on linear minimum mean square error criterion

Mondal,

Dutta

2023

New J. Phys.

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Quantum state tomography (QST) is essential for characterizing unknown quantum states. Several methods of estimating quantum states already exist and can be classified mainly into three broad classes. They are based on the criteria like maximum likelihood, linear inversion, and Bayesian framework. The Bayesian framework for QST gives a better reconstruction performance. However, the existing methods of the Bayesian frameworks are computationally extensive and, most of the time require knowledge about the prior distribution of the quantum state. In this paper, we propose a Bayesian method of QST based on the linear minimum mean square error criterion, where the prior statistics are estimated and the computational complexity is comparable to that of the linear inversion based QST method. We also propose an adaptive version based on the block estimation of parameters. Extensive numerical simulations are conducted to demonstrate its efficacy over the linear inversion-based QST regarding trace distance error metric.

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“…Quantum state tomography (QST) is one of the key ideas to characterize the target quantum state by measuring multiple copies of the same quantum state [1]. Many reliable methods of QST such as maximum likelihood (ML) based QST [2], linear regression estimation (LRE) with least squares (LS) [3], Bayesian [4], adaptive Bayesian [5,6] and self-guided state estimation [7] have already been exploited. However, reconstruction methods have advantages and disadvantages [8,9], and it is necessary to find the best-suited technique depending on the context of the quantum system.…”

Section: Introductionmentioning

confidence: 99%

A modified least squares-based tomography with density matrix perturbation and linear entropy consideration along with performance analysis

Mondal,

Dutta

2023

New J. Phys.

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Quantum state tomography identifies target quantum states by performing repetitivemeasurements on identical copies. In this paper, we have two key contributions aimed at improvingtraditional post-processing computational complexity and sample complexity of quantum tomographyprotocols. In the first case, we propose a new low-cost positivity constraint method based ondensity matrix perturbation after the least squares (LS) estimation of the density matrix. In thesecond case, we propose a new cost function with the maximum linear entropy and LS method to improvethe sample average trace distance with reasonably low sample complexity. We call it the leastsquares with the maximum entropy (LSME) method. Our proposed algorithm does not follow theiterative optimization technique, which is true for existing maximum likelihood and entropy-basedones. Performance analysis is conducted for our proposed methods by studying how they compareto the existing techniques for different sample complexities and dimensionalities. Extensive numericalsimulations have been conducted to demonstrate the advantages of the proposed tomographyalgorithms.

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Self-guided quantum state tomography for limited resources

Cited by 7 publications

References 29 publications

Pure state tomography with parallel unentangled measurements

Pure state tomography with parallel unentangled measurements

A Bayesian quantum state tomography along with adaptive frameworks based on linear minimum mean square error criterion

A modified least squares-based tomography with density matrix perturbation and linear entropy consideration along with performance analysis

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