Local optimization on pure Gaussian state manifolds

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Standard

Local optimization on pure Gaussian state manifolds. / Windt, Bennet; Jahn, Alexander; Eisert, Jens; Hackl, Lucas.

I: SciPost Physics, Bind 10, Nr. 3, 066, 2021.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Windt, B, Jahn, A, Eisert, J & Hackl, L 2021, 'Local optimization on pure Gaussian state manifolds', SciPost Physics, bind 10, nr. 3, 066. https://doi.org/10.21468/SCIPOSTPHYS.10.3.066

APA

Windt, B., Jahn, A., Eisert, J., & Hackl, L. (2021). Local optimization on pure Gaussian state manifolds. SciPost Physics, 10(3), [066]. https://doi.org/10.21468/SCIPOSTPHYS.10.3.066

Vancouver

Windt B, Jahn A, Eisert J, Hackl L. Local optimization on pure Gaussian state manifolds. SciPost Physics. 2021;10(3). 066. https://doi.org/10.21468/SCIPOSTPHYS.10.3.066

Author

Windt, Bennet ; Jahn, Alexander ; Eisert, Jens ; Hackl, Lucas. / Local optimization on pure Gaussian state manifolds. I: SciPost Physics. 2021 ; Bind 10, Nr. 3.

Bibtex

@article{2f9534b027f64cbfac52bfa2e08b747e,
title = "Local optimization on pure Gaussian state manifolds",
abstract = "We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.",
author = "Bennet Windt and Alexander Jahn and Jens Eisert and Lucas Hackl",
year = "2021",
doi = "10.21468/SCIPOSTPHYS.10.3.066",
language = "English",
volume = "10",
journal = "SciPost Physics",
issn = "2542-4653",
publisher = "SCIPOST FOUNDATION",
number = "3",

}

RIS

TY - JOUR

T1 - Local optimization on pure Gaussian state manifolds

AU - Windt, Bennet

AU - Jahn, Alexander

AU - Eisert, Jens

AU - Hackl, Lucas

PY - 2021

Y1 - 2021

N2 - We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

AB - We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

UR - http://www.scopus.com/inward/record.url?scp=85103553757&partnerID=8YFLogxK

U2 - 10.21468/SCIPOSTPHYS.10.3.066

DO - 10.21468/SCIPOSTPHYS.10.3.066

M3 - Journal article

AN - SCOPUS:85103553757

VL - 10

JO - SciPost Physics

JF - SciPost Physics

SN - 2542-4653

IS - 3

M1 - 066

ER -

ID: 261510920