Complexity Equals Action

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 AdS, 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.

published as "Holographic Complexity Equals Bulk Action?"

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• Upper bound about cross-sections inside black holes and complexity growth rate
• Complexity and Time
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• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Complexity growth for topological black holes by holographic method
• Complexity and typical microstates
• Holographic Entanglement Entropy and Complexity for D-Wave Superconductors
• Holographic complexity under a global quantum quench
• Quantum complexity and bulk timelike singularities
• Quantum complexity phase transitions in monitored random circuits
• Properties of the (Un)Complexity of Subsystems
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• A Holographic Bound for D3-Brane
• Horizons Protect Church-Turing
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• Properties of Krylov state complexity in qubit dynamics
• New Topological Gauss-Bonnet Black Holes in Five Dimensions
• Holographic entanglement entropy and subregion complexity for excited states of holographic superconductors
• Complexity from Spinning Primaries
• Complexity growth of BTZ black hole in massive gravity with a null string
• Holographic Boundary Conformal Field Theory within Horndeski Gravity
• Holographic Cavalieri Principle as a Universal relation between Holographic Complexity and Holographic Entanglement Entropy
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
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• Measuring Holographic Entanglement Entropy on a Quantum Simulator
• Bulk Action Growth for Holographic Complexity
• Interior structure of the holographic s + p superconductor and chaotic-stable transition near the black hole singularity
• Renormalized Holographic Subregion Complexity under Relevant Perturbations
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• Weighting gates in circuit complexity and holography
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• Holographic complexity growth for a charged AdS-dilaton black holes with fixed and dynamical boundary respectively
• Interface in AdS black hole spacetime
• Holographic entanglement entropy and complexity for the cosmological braneworld model
• The Complexity of Being Entangled
• Perturbative Complexity of Interacting Theory
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Holographic complexity of black non-susy D3-brane and the high temperature limit
• Holographic Entanglement Entropy, Complexity, Fidelity Susceptibility and Hierarchical UV/IR Mixing Problem in $AdS_2/\mbox{open strings}$
• Holographic Complexity from the Crofton's Formula in Lorentzian AdS${}_3$
• Complexity growth rate, grand potential and partition function
• The landscape of complexity measures in 2D gravity
• Probing Krylov Complexity in Scalar Field Theory with General Temperatures
• Late-Time Saturation of Black Hole Complexity
• Brown-Teitelboim Instantons and the First Law of Thermodynamics of (Anti) de Sitter Space
• Complexity in One- and Two-Qubit Systems
• Classical Holographic Codes
• Holographic entanglement entropy and complexity of microstate geometries
• Information theoretic measures for Lifshitz system
• Complexity Conjecture of Regular Electric Black Holes
• Complexity as a holographic probe of strong cosmic censorship
• Ultimate Limits to Computation: Anharmonic Oscillator
• Black hole interiors of homogeneous holographic solids under shear strain
• On Complexity of Holographic Flavors
• Critical distance and Crofton form in confining geometries
• Insensitivity of the complexity rate of change to the conformal anomaly and Lloyd's bound as a possible renormalization condition
• An alternative study about the geometry and the first law of thermodynamics for AdS Lovelock gravity, using the definition of conserved charges
• Entanglement Entropy with a Time-dependent Hamiltonian
• On the Complexity of a Charged Quantum Oscillator
• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• Complexity of Scalar Collapse in Anti-de Sitter Spacetime
• Warping Wormholes with Dust: a Metric Construction of the Python's Lunch
• Non-analyticity in Holographic Complexity near Critical points
• Random Circuits in the Black Hole Interior
• Holographic non-computers
• Thesis: Tensor networks for dynamic spacetimes
• Subsystem Complexity and Measurements in Holography
• Quantum fluctuation on the worldsheet of probe string in BTZ black hole
• Einstein gravity from the Einstein action: Counterterms and covariance
• Generalized volume-complexity for Lovelock black holes
• Operator Approach to Complexity : Excited States
• A note on size-momentum correspondence and chaos
• Gravity Dual of Networks
• Universal Time Evolution of Holographic and Quantum Complexity
• Quantum circuit complexity and unsupervised machine learning of topological order
• Topological Classification of a 4D AdS Black Hole with Non-Minimal Maxwell Coupling
• Reparameterization Dependence and Holographic Complexity of Black Holes
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
• Information Geometry and Holographic Correlators
• Gravity dualities of quantum distances
• How smooth is quantum complexity?
• Quantum correlation in quark-gluon medium
• What's inside a hairy black hole in massive gravity?
• What kind of "complexity" is dual to holographic complexity?
• Cosmological Complexity in K-essence
• Holographic complexity of Born-Infeld gravity
• HEE and HSC for flavors: perturbative structure in open string geometries
• Quantum state complexity and the thermodynamic arrow of time
• Holographic Complexity in Charged Accelerating Black Holes
• Finite size effect on quantum correlations
• Revisiting holographic codes with fractal-like boundary erasures
• Complexity, chaos and the moving D3-brane
• Entanglement Entropy and Complexity in Dyonic Quantum Black Holes
• Probing the Black Hole Interior with Holographic Entanglement Entropy and the Role of AdS/BCFT Correspondence
• Why is AI hard and Physics simple?
• Discrete scale invariance in holography and an argument against the complexity=action proposal
• Geometry of Entanglement
• Detecting quantum chaos via pseudo-entropy
• Computational Complexity in Analogue Gravity
• Holographic complexity of the Klebanov-Strassler background
• Entanglement entropy and complexity of singular subregions in deformed CFT
• D5-brane on topological black holes
• Complexity of Magnetization and Magnetic Simplification
• Switchback effect of holographic complexity in multiple-horizon black holes
• Purification Complexity without Purifications
• Null hypersurface caustics and super-entropic black holes
• Geometry of quantum complexity
• Toward a physically motivated notion of Gaussian complexity geometry
• Holographic complexity of rotating black holes
• Finite complexity of the de Sitter vacuum
• Holographic and QFT Complexity with angular momentum
• Interface in Kerr-AdS black hole spacetime
• Quantum origin of the Minkowski space
• Probe strings on AdS accelerating black holes
• Holographic Interpretation of Relative State Complexity
• Quantum Circuit Complexity as a Measure of Particle Creation in Bouncing Cosmologies
• Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory
• Geometry Perspective Of Estimating Learning Capability Of Neural Networks
• Entanglement Entropy and Complexity of Multicomponent Universe from Holography
• Inverse anisotropic catalysis and complexity
• Comparing quantum complexity and quantum fidelity
• Extended Relativity: Beyond
• Geometric measure of quantum complexity in cosmological systems
• Circuit Complexity for Coherent-Thermal States in Bosonic String Theory
• Quantum Information Approaches to Quantum Gravity
• Time dependent Interface in AdS Black Hole Spacetime
• Spread Complexity of High Energy Neutrino Propagation over Astrophysical Distances
• Cost of holographic path integrals
• Developments in non-relativistic field theory and complexity
• Thermodynamics of non-linearly charged Anti-de Sitter black holes in four-dimensional Critical Gravity
• On Maximum Complexity in Holography
• Quantum chaos measures for Floquet dynamics
• Spread complexity and localization in $\mathcal{P}\mathcal{T}$-symmetric systems
• The quantum mass gap of extremal black holes