Complexity, action, and black holes
By Adam R. Brown, Daniel A. Roberts, L. Susskind, Brian Swingle, Ying Zhao. 2015
692 citations recorded by the source corpus.
In an earlier paper "Complexity Equals Action" we conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the `Wheeler-DeWitt' patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are the fastest computers in nature.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/db282be619bad33f36cb8124064936d1382a92bc
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Citations in the corpus
- Geometry of Krylov complexity (2021, background): “On one hand, linking these two ideas is important from a physics point of view, given the recent activity concerning the relation between complexity and black hole physics [36–39, 43, 47].”
- Second law of quantum complexity (2017, methodology): “This is discussed in detail in [24] and also in [20].”
- Holographic complexity in Vaidya spacetimes. Part I (2018, background): “29) is always smaller than the corresponding result [29, 30] for the eternal black hole geometry with any d and for both k = 0 and +1.”
- Circuit complexity for free fermions (2018, background): “(CA) conjecture identies the complexity with the gravitational action evaluated on a particular bulk region, known as the Wheeler-DeWitt (WDW) patch, which is again anchored on a boundary time slice [5,6].1 Both of the holographic complexity conjectures point out new classes of interesting gravitati”
- Chaos and complexity by design (2016, background): “A direct connection between complexity and black hole geometry was first proposed by Susskind [72, 73], which culminated in proposals that the interior of the black hole geometry is holographically dual to the spatial volume [74] or the spacetime action [75, 76].”
- On the time dependence of holographic complexity (2017, methodology): “In this section, we study the time evolution of holographic complexity using the complexity=action (CA) conjecture [7, 8] for (neutral) eternal AdS black holes in d + 1 dimensions.”
- Circuit complexity in quantum field theory (2017, background): “This identifies the complexity of the boundary state with the gravitational action evaluated on a bulk region known as the Wheeler-DeWitt (WDW) patch [15, 16]:”
- Comments on holographic complexity (2016, methodology): “These coefficients also contain dimensionless parameters characterizing the underlying CFT, e.g., CT ∼ Ld−1/GN in the present case where the bulk is described by Einstein gravity.11 The leading divergence appearing with the CV duality is proportional to the volume of the boundary time slice, i.e., C”
- Complexity of formation in holography (2016, methodology): “’ Hence applying the complexity=action proposal [1, 2], we begin by evaluating the action of the WDW patch with tL = 0 = tR, shown in figure 1, to determine the complexity of the thermofield double state (1.”
- Quantum complexity and negative curvature (2016, background): “In particular, this functional form will be true if we use ERB volume [1, 3] or action [12, 13].”
- Circuit complexity for coherent states (2018, background): “the gravitational dual of the circuit complexity in the boundary theory. In particular, there are two proposals for ‘holographic complexity’: complexity=volume (CV) [15,16] and complexity=action (CA) [17,18]. The CV conjecture states that the complexity of the boundary state is proportional to the v”
- Chaos, complexity, and random matrices (2017, background): “In the past few years, quantum complexity has been considered in holography as a possible CFT observable(20) to study the late-time dynamics of the AdS black holes [50, 51].”
- Complexity and entanglement for thermofield double states (2018, background): “20] proposal states that the complexity is given by the codimension-one volume of the maximal spacelike slice that connects the left and right CFTs through the bulk. The \complexity=action" (CA) [21,22] conjecture instead suggests that a more appropriate bulk dual is given by the gravitational ”
- Emergent Gravity and the Dark Universe (2016, background): “pacetime. Note that these arguments are closely related to the discussions that led to the rewall paradox [25], EPR=ER proposal [26] and the ideas of fast scrambling [29] and computational complexity [41]. The size of the Hilbert space of bulk states is exactly given by the horizon area, since this ”
- Quantum extremal islands made easy. Part II. Black holes on the brane (2020, background): “On a related note, one might also study the complexity of these brane configurations, for example, using the higher-dimensional bulk to probe holographic complexity conjectures [145–148], e.”
- Noether charge, black hole volume, and complexity (2016, methodology): “In the second part of the paper (sections 3 and 4), we will relate the thermodynamic volume (and also the Smarr relation) to the complexity as per the proposals in [25, 26].”