dc.contributor.author
Windt, Bennet
dc.contributor.author
Jahn, Alexander
dc.contributor.author
Eisert, Jens
dc.contributor.author
Hackl, Lucas
dc.date.accessioned
2021-10-28T10:13:47Z
dc.date.available
2021-10-28T10:13:47Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/32420
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-32144
dc.description.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.
en
dc.format.extent
53 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Gaussian states
en
dc.subject
Gaussian purifications
en
dc.subject
local optimization algorithm
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::530 Physik
dc.title
Local optimization on pure Gaussian state manifolds
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
066
dcterms.bibliographicCitation.doi
10.21468/SciPostPhys.10.3.066
dcterms.bibliographicCitation.journaltitle
SciPost Physics
dcterms.bibliographicCitation.number
3
dcterms.bibliographicCitation.volume
10
dcterms.bibliographicCitation.url
https://doi.org/10.21468/SciPostPhys.10.3.066
refubium.affiliation
Physik
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Dahlem Center für komplexe Quantensysteme

refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
2542-4653
refubium.resourceType.provider
WoS-Alert