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
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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.
Cited by 15
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
- 1 Julius-Maximilians-Universität Würzburg / University of Würzburg
- 2 Würzburg-Dresden Cluster of Excellence [ct.qmat]
- 3 Instituto de Física Teórica / Institute for Theoretical Physics [IFT]
- 4 Universiteit Gent / Ghent University
- 5 Max-Planck-Institut für Gravitationsphysik / Max Planck Institute for Gravitational Physics [AEI]
- 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])