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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Quantum speed limits on operator flows and correlation functions
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Complexity measures in QFT and constrained geometric actions
TL;DR: In this article, the conditions under which, given a generic quantum system, complexity metrics provide actual lower bounds to the circuit complexity associated to a set of quantum gates are studied and a hierarchy of cost functions and considerably reduces the list of candidate complexity measures.
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Revisit on holographic complexity in two-dimensional gravity
TL;DR: In this article, the late-time growth rate of various holographic complexity conjectures for neutral and charged AdS black holes with single or multiple horizons in two dimensional (2D) gravity like JT-like gravity was revisited.
Complexity equals anything II
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Complexity and action for warped AdS black holes
TL;DR: In this paper, the Complexity=Action conjecture for black holes in Warped AdS$_3$ space is studied for non-rotating and rotating cases. But the asymptotic growth rate is equal to the Hawking temperature times the Bekenstein-Hawking entropy.
References
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