Complexity, action, and black holes

Abstract

Our earlier paper "Complexity Equals Action" 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.

55+14 pages, many figures. v2: (so many) typos fixed, references added

References in corpus (7)

• Black holes as mirrors: quantum information in random subsystems
• Complexity and Shock Wave Geometries
• Chaos in quantum channels
• Quantum Computation as Geometry
• Relative entropy and the Bekenstein bound
• Switchbacks and the Bridge to Nowhere
• Disrupting Entanglement of Black Holes

Cited by in corpus (459)

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• Quantum Extremal Islands Made Easy, PartIII: Complexity on the Brane
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• The Complexity Geometry of a Single Qubit
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• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
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• Complexity Growth Rate in Lovelock Gravity
• Evolution of Complexity Following a Global Quench
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• Gravity Degrees of Freedom on a Null Surface
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• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
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• Chaos of Particle Motion near the Black Hole with Quasi-topological Electromagnetism
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• Circuit Complexity across a Topological Phase Transition
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
• Holo-ween
• On holographic time-like entanglement entropy
• On the time dependence of holographic complexity in a dynamical Einstein-dilaton model
• Aspects of The First Law of Complexity
• Holographic complexity and action growth in massive gravities
• Entanglement, quantum randomness, and complexity beyond scrambling
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• Action growth rate for a higher curvature gravitational theory
• Connecting Fisher information to bulk entanglement in holography
• Divergences in the rate of complexification
• Testing Holographic Conjectures of Complexity with Born-Infeld Black Holes
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• Dynamical phase transitions in sampling complexity
• Circuit Complexity From Cosmological Islands
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• Complexity and Behind the Horizon Cut Off
• Complexity for Charged Thermofield Double States
• Wormholes & Holography: An Introduction
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• Holographic spacetime, black holes and quantum error correcting codes: A review
• Holographic local quench and effective complexity
• The connection between holographic entanglement and complexity of purification
• Probing the entanglement of operator growth
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• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Holographic Complexity in dS${}_{d+1}$
• Lorentzian threads as 'gatelines' and holographic complexity
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• Spread complexity in saddle-dominated scrambling
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• Holographic Complexity of Quantum Black Holes
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• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Quantum-first gravity
• Time evolution of the complexity in chaotic systems: concrete examples
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• Topological shadows and complexity of islands in multiboundary wormholes
• Holographic Complexity and Thermodynamic Volume
• Trans-IR Flows to Black Hole Singularities
• Circuit complexity for generalised coherent states in thermal field dynamics
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
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• Holographic Subregion Complexity for Singular Surfaces
• Binding Complexity and Multiparty Entanglement
• Interior Structure and Complexity Growth Rate of Holographic Superconductor from M-Theory
• Holographic Complexity Growth Rate in Horndeski Theory
• Thoughts on Holographic Complexity and its Basis-dependence
• Mixed s-sourcery: Building many-body states using bubbles of Nothing
• Conformal bootstrap to Rényi entropy in 2D Liouville and super-Liouville CFTs
• On Some Universal Features of the Holographic Quantum Complexity of Bulk Singularities
• General Bounds on Holographic Complexity
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• Learning quantum states and unitaries of bounded gate complexity
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• The Speed of Quantum Information Spreading in Chaotic Systems
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• Comments on black hole interiors and modular inclusions
• On Complexity Growth in Minimal Massive 3D Gravity
• SVD Entanglement Entropy
• Complexity growth rate during phase transitions
• Complexity and Momentum
• Bag-of-gold spacetimes, Euclidean wormholes, and inflation from domain walls in AdS/CFT
• Nonanalyticity of circuit complexity across topological phase transitions
• Complexity and phase transitions in a holographic QCD model
• Holographic Purification Complexity
• Momentum/Complexity Duality and the Black Hole Interior
• A defect in holographic interpretations of tensor networks
• Complexity and Boost Symmetry
• Butterflies with rotation and charge
• Chaos and Complexity for Inverted Harmonic Oscillators
• Bounds on quantum evolution complexity via lattice cryptography
• Action Growth in $f\left(R\right)$ Gravity
• Charged Complexity and the Thermofield Double State
• Mixed State Entanglement for Holographic Axion Model
• Resource theory of quantum uncomplexity
• Fast optimization algorithms and the cosmological constant
• Lovelock action with nonsmooth boundaries
• Complexity/Action duality of shock wave geometry in a massive gravity theory
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• Complexity growth of rotating black holes with a probe string
• On volume subregion complexity in Vaidya spacetime
• Holographic Complexity and Charged Scalar Fields
• Holographic complexity: A tool to probe the property of reduced fidelity susceptibility
• Holographic complexity and thermodynamics of AdS black holes
• A Quantum Complexity Lowerbound from Differential Geometry
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Investigating two counting methods of the holographic complexity
• Thermodynamic Information Geometry and Complexity Growth of Warped AdS Black Hole and the WAdS${}_3$/CFT${}_2$ Correspondence
• Modified "complexity equals action" conjecture
• Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductor
• On Complexity of Jackiw-Teitelboim Gravity
• Subsystem complexity after a global quantum quench
• Quasinormal modes, greybody factors and thermodynamics of four dimensional AdS black holes in Critical Gravity
• On subregion action complexity in AdS${}_3$ and in the BTZ black hole
• On the Role of Counterterms in Holographic Complexity
• Holographic complexity in charged Vaidya black hole
• Spacetime as a quantum circuit
• Proof of a Momentum/Complexity Correspondence
• Dear Qubitzers, GR=QM
• A Generalized Momentum/Complexity Correspondence
• Evolutions of entanglement and complexity after a thermal quench in massive gravity theory
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Complexity growth and shock wave geometry in AdS-Maxwell-power-Yang-Mills theory
• Decoherence, Entanglement Negativity and Circuit Complexity for Open Quantum System
• On the time dependence of holographic complexity for charged AdS black holes with scalar hair
• Volume complexity for Janus ${\mathrm{AdS}}_3$ geometries
• Action growth for black holes in modified gravity
• Computing spacetime
• Kasner interiors from analytic hairy black holes
• Emergent Einstein Equation in p-adic CFT Tensor Networks
• Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning
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• Holographic complexity of local quench at finite temperature
• More on Complexity in Finite Cut Off Geometry
• Holevo Information and Ensemble Theory of Gravity
• Holographic complexity growth in a FLRW universe
• de Sitter as a Resonance
• Complexity in the Lipkin-Meshkov-Glick Model
• Volume complexity of dS bubbles
• Terminal Holographic Complexity
• Holographic subregion complexity under thermal quench in Einstein-Maxwell-Axions theory with momentum relaxation
• Regularizations of Action-Complexity for a Pure BTZ Black Hole Microstate
• Rotating black hole with a probe string in Horndeski Gravity
• Complexity, Information Geometry, and Loschmidt Echo near Quantum Criticality
• Null boundary terms for Lanczos-Lovelock gravity
• Energy cost of entanglement extraction in complex quantum systems
• Magnetotransport and Complexity of Holographic Metal-Insulator Transitions
• Complexity-action of subregions with corners
• Action complexity in the presence of defects and boundaries
• Optimal uncertainty relations in a modified Heisenberg algebra
• Evolution of Holographic Complexity Near Critical Point
• Complexity of operators generated by quantum mechanical Hamiltonians
• Mixed State Entanglement and Thermal Phase Transitions
• Time dependence of complexity for Lovelock black holes
• Circuit Complexity in Topological Quantum Field Theory
• Bulk geometry from entanglement entropy of CFT
• Holographic subregion complexity of boosted black brane and Fisher information
• Chemistry and Complexity for Solitons in AdS${}_5$
• Dynamics for holographic codes
• Complexity of Hyperscaling Violating Theories at Finite Cutoff
• Holographic complexity of charged Taub-NUT-AdS black holes
• Complexity in a moving mirror model
• Revisit on holographic complexity in two-dimensional gravity
• Complexity Growth in Flat Spacetimes
• Holographic complexity for black branes with momentum relaxation
• Computational pseudorandomness, the wormhole growth paradox, and constraints on the AdS/CFT duality
• Anisotropic Flows into Black Holes
• Krylov Complexity of Open Quantum Systems: From Hard Spheres to Black Holes
• Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Entwinement as a possible alternative to complexity
• Holographic complexity for Lifshitz system
• Krylov complexity of deformed conformal field theories
• Universality in long-distance geometry and quantum complexity
• Non-perturbative Overlaps in JT Gravity: From Spectral Form Factor to Generating Functions of Complexity
• Holographic complexity of the electromagnetic black hole
• Topological and Time Dependence of the Action-Complexity Relation
• Bulk reconstruction of metrics inside black holes by complexity
• Volume complexity for the non-supersymmetric Janus AdS${}_5$ geometry
• Interior Volume of Banados-Teitelboim-Zanelli Black Hole
• Primordial Gravitational Wave Circuit Complexity
• Black Holes and Complexity Classes
• Decoherence and Microscopic Diffusion at SYK
• Geometrical tools for embedding fields, submanifolds, and foliations
• Circuit complexity near critical points
• Maximal volume behind horizons without curvature singularity
• Chaos and multifold complexity for an inverted harmonic oscillator
• Quantum bit threads and holographic entanglement
• Comments on Joint Terms in Gravitational Action
• Complexity and Multi-boundary Wormholes
• Holographic complexity of Born-Infeld black holes
• Holographic Complexity of LST and Single Trace $T\bar{T}$
• Complexity growth in Gubser-Rocha models with momentum relaxation
• Holographic complexity in general quadratic curvature theory of gravity
• Holographic complexity: braneworld gravity versus the Lloyd bound
• Charged Fuzzy Dark Matter Black Holes
• Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Circuit Complexity in an interacting quenched Quantum Field Theory
• Entanglement entropy and monotones in scattering process
• Subregion complexity in holographic thermalization with dS boundary
• Holographic Complexity Bounds
• Python's Lunches in Jackiw-Teitelboim gravity with matter
• de Sitter Harmonies: Cosmological Spacetimes as Resonances
• Non-Conformality, Subregion Complexity and Meson Binding
• Entanglement dynamics of thermofield double states in integrable models
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Bosonic and fermionic Gaussian states from Kähler structures
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• Complexity Growth Following Multiple Shocks
• Effects of quintessence dark energy on the action growth and butterfly velocity
• Complexity-constrained quantum thermodynamics
• A note on holographic subregion complexity and QCD phase transition
• Holographic Entanglement Entropy, Subregion Complexity and Fisher Information metric of `black' Non-SUSY D3 Brane
• The Interior Volume of Kerr-AdS Black Holes
• On the Complexity of a $2+1$--dimensional Holographic Superconductor
• Collisions of localized shocks and quantum circuits
• Subregion complexity and confinement-deconfinement transition in a holographic QCD model
• On Volume Subregion Complexity in Non-Conformal Theories
• Holographic Complexity in FRW Spacetimes
• Holographic entanglement entropy for charged accelerating AdS black holes
• Sectional curvatures distribution of complexity geometry
• Holographic subregion complexity of a 1+1 dimensional $p$-wave superconductor
• Quantum Information Metric on $\mathbb{R}\times S^{d-1}$
• Universal Pieces of Holographic Entanglement Entropy and Holographic Subregion Complexity
• Complexity growth of massive black hole with a probe string
• The Cosmological Switchback Effect II
• Quantum complexity and the virial theorem
• Complexity via Replica Trick
• Subsystem complexity after a local quantum quench
• Complexity measures in QFT and constrained geometric actions
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Complexity, scaling, and a phase transition
• Holographic complexity of braneworld in Horndeski gravity
• Reparameterization Dependence is Useful for Holographic Complexity
• Circuit complexity in proca theory
• Complexity and uncomplexity during energy injection
• Action Complexity for Semi-Classical Black Holes
• Probes of holographic thermalization in a simple model with momentum relaxation
• Holographic complexity of rotating black holes with conical deficits
• Action complexity of charged black holes with higher derivative interactions
• Diving inside holographic metals
• Holographic Complexity for disentangled states
• Geometric quantum complexity of bosonic oscillator systems
• Holographic complexity of hyperbolic black holes
• Quantum Spread Complexity in Neutrino Oscillations
• Complexity Growth, Butterfly Velocity and Black hole Thermodynamics
• Complexity and scaling in quantum quench in $1+1$ dimensional fermionic field theories
• Complexity and Time
• Action Growth of Dyonic Black Holes and Electromagnetic Duality
• Holographic Complexity in a Charged Supersymmetric Black Holes
• Entanglement wedge method, out-of-time-ordered correlators, and pole skipping
• Holographic networks for (1+1)-dimensional de Sitter spacetime
• Upper bound about cross-sections inside black holes and complexity growth rate
• Negative Complexity of Formation: the Compact Dimensions Strike Back
• Mixed state information theoretic measures in boosted black brane
• Polynomial Equivalence of Complexity Geometries
• Saturation and recurrence of quantum complexity in random local quantum dynamics
• Krylov Complexity of Fermionic and Bosonic Gaussian States
• Time-independent wormholes
• Evolution of circuit complexity in a harmonic chain under multiple quenches
• Complexity and quenches in models with three and four spin interactions
• Holographic Complexity and Phase Transition for AdS Black Holes
• Complexity growth for topological black holes by holographic method
• Quantum complexity and bulk timelike singularities
• Holographic Complexity of LST and Single Trace $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$ deformations
• Complexity and typical microstates
• A Holographic Bound for D3-Brane
• TNSPackage: A Fortran2003 library designed for tensor network state methods
• Note on stability and holographic subregion complexity
• Constraining higher order gravities with subregion duality
• Real space circuit complexity as a probe of phase diagrams
• Properties of Krylov state complexity in qubit dynamics
• Weighting gates in circuit complexity and holography
• Bulk Action Growth for Holographic Complexity
• Renormalized Holographic Subregion Complexity under Relevant Perturbations
• Complexity growth of BTZ black hole in massive gravity with a null string
• Effects of the acceleration on holographic complexity
• Thermodynamic and Holographic Information Dual to Volume
• Quantum algorithms for conformal bootstrap
• Complexity for link complement States in Chern Simons Theory
• New Topological Gauss-Bonnet Black Holes in Five Dimensions
• Holographic Cavalieri Principle as a Universal relation between Holographic Complexity and Holographic Entanglement Entropy
• Order $p$ quantum Wasserstein distances from couplings
• Generalized holographic complexity of rotating black holes
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
• Minimal Purifications, Wormhole Geometries, and the Complexity=Action Proposal
• Holographic Complexity of Subregions in the Hyperscaling Violating Theories
• Circuit Complexity in $U(1)$ Gauge Theory
• Complexity from Spinning Primaries
• Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality
• Holographic complexity for nonlinearly charged Lifshitz black holes
• Quasinormal Modes and the Switchback Effect in Schwarzschild-de Sitter
• Complexity for superconformal primaries from BCH techniques
• Holographic information theoretic quantities for Lifshitz black hole
• Towards a theory of machine learning
• Perturbative Complexity of Interacting Theory
• Interface in AdS black hole spacetime
• Towards a Fisher-information description of complexity in de Sitter universe
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• More on Holographic Volumes, Entanglement, and Complexity
• Holographic complexity growth for a charged AdS-dilaton black holes with fixed and dynamical boundary respectively
• Position dependence of Nielsen complexity for the Thermofield double state
• The Complexity of Being Entangled
• Non-analyticity in Holographic Complexity near Critical points
• Late-Time Saturation of Black Hole Complexity
• On the Complexity of a Charged Quantum Oscillator
• Holographic Entanglement Entropy, Complexity, Fidelity Susceptibility and Hierarchical UV/IR Mixing Problem in $AdS_2/\mbox{open strings}$
• Warping Wormholes with Dust: a Metric Construction of the Python's Lunch
• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• Complexity of Scalar Collapse in Anti-de Sitter Spacetime
• Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum
• Complexity as a holographic probe of strong cosmic censorship
• Insensitivity of the complexity rate of change to the conformal anomaly and Lloyd's bound as a possible renormalization condition
• Complexity in One- and Two-Qubit Systems
• How Not to Extract Information From Black Holes: Cosmic Censorship as a Guiding Principle
• Random Circuits in the Black Hole Interior
• Complexity Conjecture of Regular Electric Black Holes
• Holographic Complexity from the Crofton's Formula in Lorentzian AdS${}_3$
• Holographic entanglement entropy and complexity of microstate geometries
• On Complexity of Holographic Flavors
• Information theoretic measures for Lifshitz system
• Complexity growth rate, grand potential and partition function
• Holographic complexity of black non-susy D3-brane and the high temperature limit
• Brown-Teitelboim Instantons and the First Law of Thermodynamics of (Anti) de Sitter Space
• Holographic complexity of Born-Infeld gravity
• Operator Approach to Complexity : Excited States
• Thesis: Tensor networks for dynamic spacetimes
• A note on size-momentum correspondence and chaos
• HEE and HSC for flavors: perturbative structure in open string geometries
• Quantum correlation in quark-gluon medium
• Reparameterization Dependence and Holographic Complexity of Black Holes
• Resource and stability near a critical point from the quantum information perspective
• Quantum fluctuation on the worldsheet of probe string in BTZ black hole
• Krylov complexity of purification
• Generalized volume-complexity for Lovelock black holes
• Holographic non-computers
• Universal Time Evolution of Holographic and Quantum Complexity
• Quantum circuit complexity and unsupervised machine learning of topological order
• Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity
• How smooth is quantum complexity?
• Cosmological Complexity in K-essence
• Complexity Growth of Dyonic Black holes with Quartic Field Strength Corrections
• Complexity, chaos and the moving D3-brane
• Finite size effect on quantum correlations
• Interface in Kerr-AdS black hole spacetime
• Geometry of quantum complexity
• Detecting quantum chaos via pseudo-entropy
• Switchback effect of holographic complexity in multiple-horizon black holes
• Why is AI hard and Physics simple?
• Entanglement entropy and complexity of singular subregions in deformed CFT
• Complexity vs. Vorticity
• Holographic complexity of the Klebanov-Strassler background
• Holographic complexity of rotating black holes
• D5-brane on topological black holes
• Probing the Black Hole Interior with Holographic Entanglement Entropy and the Role of AdS/BCFT Correspondence
• Toward a physically motivated notion of Gaussian complexity geometry
• Complexity of Magnetization and Magnetic Simplification
• Holographic and QFT Complexity with angular momentum
• Holographic Complexity in Charged Accelerating Black Holes
• Holographic Subregion Complexity and Fidelity Susceptibility in Noncommutative Yang--Mills Theory
• Holographic Interpretation of Relative State Complexity
• Entanglement Entropy and Complexity of Multicomponent Universe from Holography
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Spread Complexity of High Energy Neutrino Propagation over Astrophysical Distances
• Probe strings on AdS accelerating black holes
• Circuit Complexity for Coherent-Thermal States in Bosonic String Theory
• Quantum entanglement and the geometry of spacetime
• On Maximum Complexity in Holography
• Quantum Information Approaches to Quantum Gravity
• Time dependent Interface in AdS Black Hole Spacetime
• Developments in non-relativistic field theory and complexity
• Kinematics of Horizon and Singularity and IR/UV Mixing in AdS
• Quantum Circuit Complexity as a Measure of Particle Creation in Bouncing Cosmologies
• Thermodynamics of non-linearly charged Anti-de Sitter black holes in four-dimensional Critical Gravity