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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Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
Pawel Caputa,Nilay Kundu,Masamichi Miyaji,Tadashi Takayanagi,Tadashi Takayanagi,Kento Watanabe +5 more
TL;DR: In this paper, an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions is proposed, where the optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the pathintegrals.
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On the Time Dependence of Holographic Complexity
Dean Carmi,Dean Carmi,Shira Chapman,Hugo Marrochio,Hugo Marrochio,Robert C. Myers,Sotaro Sugishita,Sotaro Sugishita +7 more
TL;DR: In this paper, the authors evaluate the full time dependence of holographic complexity in various eternal black hole backgrounds using both the complexity=action (CA) and the complexity-volume (CV) conjectures and conclude that the rate of change of complexity is a monotonically increasing function of time, which saturates from below to a positive constant in the late time limit.
Journal ArticleDOI
Second law of quantum complexity
Adam R. Brown,Leonard Susskind +1 more
TL;DR: In this paper, the second law of complexity of a quantum system was shown to be equivalent to the Kolmogorov complexity of the quantum Hamiltonian, and it was shown that the expected pattern of growth of the complexity of quantum system parallels the growth of entropy of the classical system.
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Noether charge, black hole volume, and complexity
TL;DR: In this paper, the authors apply the Noether charge formalism of Iyer and Wald to study the thermodynamic volumes of AdS black holes and discuss the role of thermodynamics in complexity = action for a number of black hole solutions, and then point out the possibility of an alternate proposal, which they dub complexity = volume 2.0.
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Circuit complexity in fermionic field theory
TL;DR: In this paper, the authors define and calculate versions of complexity for free fermionic quantum field theories in 1 + 1 and 3 + 1 dimensions, adopting Nielsen's geodesic perspective in the space of circuits.
References
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