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Greedy reconstruction algorithm for the identification of spin distribution

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2021

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Salomon, Julien
Sugny, Dominique

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https://doi.org/10.1103/PhysRevA.104.063112
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http://arxiv.org/abs/2108.11745

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Physical Review A. American Physical Society (APS). 2021, 104(6), 063112. ISSN 2469-9926. eISSN 2469-9934. Available under: doi: 10.1103/PhysRevA.104.063112

Zusammenfassung

We propose a greedy reconstruction algorithm to find the probability distribution of a parameter characterizing an inhomogeneous spin ensemble in nuclear magnetic resonance. The identification is based on the application of a number of constant control processes during a given time for which the final ensemble magnetization vector is measured. From these experimental data, we show that the identifiability of a piecewise constant approximation of the probability distribution is related to the invertibility of a matrix, which depends on the different control protocols applied to the system. The algorithm aims to design specific controls which ensure that this matrix is as far as possible from a singular matrix. Numerical simulations reveal the efficiency of this algorithm in different examples. A systematic comparison with respect to random constant pulses is done.

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510 Mathematik

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ISO 690BUCHWALD, Simon, Gabriele CIARAMELLA, Julien SALOMON, Dominique SUGNY, 2021. Greedy reconstruction algorithm for the identification of spin distribution. In: Physical Review A. American Physical Society (APS). 2021, 104(6), 063112. ISSN 2469-9926. eISSN 2469-9934. Available under: doi: 10.1103/PhysRevA.104.063112
BibTex
@article{Buchwald2021Greed-56047,
  year={2021},
  doi={10.1103/PhysRevA.104.063112},
  title={Greedy reconstruction algorithm for the identification of spin distribution},
  number={6},
  volume={104},
  issn={2469-9926},
  journal={Physical Review A},
  author={Buchwald, Simon and Ciaramella, Gabriele and Salomon, Julien and Sugny, Dominique},
  note={Article Number: 063112}
}
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