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Exact Gravity Duals for Simple Quantum Circuits

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

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Submission summary

Authors (as Contributors): Mario Flory · Marius Gerbershagen · Michal P. Heller
Submission information
Preprint link: scipost_202203_00020v2
Date accepted: 2022-07-25
Date submitted: 2022-06-23 10:21
Submitted by: Gerbershagen, Marius
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. 13, 061 (2022)

List of changes

- implemented the requested changes around equation (40)
- fixed some typos in appendix A

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