Tensor-network approach for quantum metrology in many-body quantum systems

authored by: Krzysztof Chabuda, Jacek Dziarmaga, Tobias J. Osborne, Rafał Demkowicz-Dobrzański
Abstract: Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility—a parameter widely used to study phase transitions.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): University of Warsaw
Jagiellonian University
Type: Article
Journal: Nature Communications
Volume: 11
Pages: 250
ISSN: 2041-1723
Publication date: 14.01.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Chemistry(all), Biochemistry, Genetics and Molecular Biology(all), Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.1038/s41467-019-13735-9 (Access: Open)
https://doi.org/10.15488/10595 (Access: Open)

BibTeX

@article{32905ae380ce4e52850f83dd2a928ac0,
title = "Tensor-network approach for quantum metrology in many-body quantum systems",
abstract = "Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide a comprehensive framework exploiting matrix product operators (MPO) type tensor networks for quantum metrological problems. The maximal achievable estimation precision as well as the optimal probe states in previously inaccessible regimes can be identified including models with short-range noise correlations. Moreover, the application of infinite MPO (iMPO) techniques allows for a direct and efficient determination of the asymptotic precision in the limit of infinite particle numbers. We illustrate the potential of our framework in terms of an atomic clock stabilization (temporal noise correlation) example as well as magnetic field sensing (spatial noise correlations). As a byproduct, the developed methods may be used to calculate the fidelity susceptibility—a parameter widely used to study phase transitions.",
author = "Krzysztof Chabuda and Jacek Dziarmaga and Osborne, {Tobias J.} and Rafa{\l} Demkowicz-Dobrza{\'n}ski",
note = "Funding information: We would like to thank Marek M. Rams, David Layden, Maciej Lewenstein, Shi-Ju Ran, Piet O. Schmidt, and Ian D. Leroux for fruitful discussions. We are also indebt to Marek M. Rams for sharing with us the data from ref. 43. K.Ch. and R.D.D. acknowledge support from the National Science Center (Poland) grant No. 2016/22/E/ST2/00559. Work of J.D. was funded by the National Science Center (Poland) together with European Union through QuantERA ERA NET program 2017/25/Z/ST2/03028. T.J.O. was supported, in part, by the DFG through SFB 1227 (DQmat), the RTG 1991, and the cluster of excellence EXC 2123 QuantumFrontiers.",
year = "2020",
month = jan,
day = "14",
doi = "10.1038/s41467-019-13735-9",
language = "English",
volume = "11",
pages = "250",
journal = "Nature Communications",
issn = "2041-1723",
publisher = "Nature Publishing Group",
number = "1",
}