Exact Gravity Duals for Simple Quantum Circuits

Erdmenger, Johanna; Flory, Mario; Gerbershagen, Marius; Heller, Michal P.; Weigel, Anna-Lena

doi:10.21468/SciPostPhys.13.3.061

SciPost Physics

Exact Gravity Duals for Simple Quantum Circuits

Johanna Erdmenger, Mario Flory, Marius Gerbershagen, Michal P. Heller, Anna-Lena Weigel

SciPost Phys. 13, 061 (2022) · published 22 September 2022

doi: 10.21468/SciPostPhys.13.3.061
pdf
Submissions/Reports

Abstract

Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion of a class of circuits that, when acting on a given reference state, all produce a desired target state. In the present work we build on studies of circuits performing local conformal transformations in general two-dimensional conformal field theories and construct the exact gravity dual to such circuits. In our approach to holographic complexity, the gravity dual to the optimal circuit is the one that minimizes an externally chosen cost assigned to each circuit. Our results provide a basis for studying exact gravity duals to circuit costs from first principles.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.3.061
TI  - Exact Gravity Duals for Simple Quantum Circuits
PY  - 2022/09/22
UR  - https://scipost.org/SciPostPhys.13.3.061
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 3
SP  - 061
A1  - Erdmenger, Johanna
AU  - Flory, Mario
AU  - Gerbershagen, Marius
AU  - Heller, Michal P.
AU  - Weigel, Anna-Lena
AB  - Holographic complexity proposals have sparked interest in quantifying the cost of state preparation in quantum field theories and its possible dual gravitational manifestations. The most basic ingredient in defining complexity is the notion of a class of circuits that, when acting on a given reference state, all produce a desired target state. In the present work we build on studies of circuits performing local conformal transformations in general two-dimensional conformal field theories and construct the exact gravity dual to such circuits. In our approach to holographic complexity, the gravity dual to the optimal circuit is the one that minimizes an externally chosen cost assigned to each circuit. Our results provide a basis for studying exact gravity duals to circuit costs from first principles.
ER  -

@Article{10.21468/SciPostPhys.13.3.061,
	title={{Exact Gravity Duals for Simple Quantum Circuits}},
	author={Johanna Erdmenger and Mario Flory and Marius Gerbershagen and Michal P. Heller and Anna-Lena Weigel},
	journal={SciPost Phys.},
	volume={13},
	pages={061},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.3.061},
	url={https://scipost.org/10.21468/SciPostPhys.13.3.061},
}

Cited by 12

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ ² Johanna Erdmenger,
³ Mario Flory,
¹ ² Marius Gerbershagen,
⁴ ⁵ Michal P. Heller,
¹ ² Anna-Lena Weigel

Funders for the research work leading to this publication

Alexander von Humboldt-Stiftung / Alexander von Humboldt Foundation
Bundesministerium für Bildung und Forschung / Federal Ministry of Education and Research [BMBF]
Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
Ministerio de Ciencia e Innovación
Secretaría de Estado de Investigacion, Desarrollo e Innovacion (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])