Holographic Complexity Equals Bulk Action
TLDR
The hypothesis that black holes are the fastest computers in nature is discussed and the conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that is called a Wheeler-DeWitt patch is illustrated.Abstract:
We conjecture that the quantum complexity of a holographic state is dual to the action of a certain spacetime region that we call a Wheeler-DeWitt patch. We illustrate and test the conjecture in the context of neutral, charged, and rotating black holes in anti-de Sitter spacetime, as well as black holes perturbed with static shells and with shock waves. This conjecture evolved from a previous conjecture that complexity is dual to spatial volume, but appears to be a major improvement over the original. In light of our results, we discuss the hypothesis that black holes are the fastest computers in nature.read more
Citations
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Holographic complexity: A tool to probe the property of reduced fidelity susceptibility
Wen-Cong Gan,Fu-Wen Shu +1 more
TL;DR: In this article, the RFS/HC duality between reduced fidelity susceptibility and holographic complexity was investigated and a quantitative proof of the duality was given by performing both holographic and field theoretical computations.
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Complexity of AdS$_5$ black holes with a rotating string
TL;DR: The system contains a particle moving on the boundary of AdS that corresponds to the insertion of a fundamental string in AdS_5 bulk spacetime, which gives a hint for defining complexity in quantum field theories.
Posted Content
Black Holes and Complexity Classes
TL;DR: It is known that the longer the classical general relativity can describe the interior geometry of black holes, the more limited are quantum computers as discussed by the authors, which is a result of unpublished work done by Scott Aaronson and himself.
Journal ArticleDOI
Circuit complexity for generalized coherent states in thermal field dynamics
TL;DR: This work finds that even though the coherent thermal (CT) state cannot be fully determined by the symmetric two-point function, the circuit complexity can still be computed in the framework of the covariance matrix formalism by properly enlarging the covariances matrix.
Journal ArticleDOI
WdW-patches in AdS$_{3}$ and complexity change under conformal transformations II
TL;DR: In this article, the authors studied the complexity of the CFT$_2$ groundstate changes under a small local conformal transformation according to the action (CA) proposal.
References
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