Complexity of Formation in Holography

Abstract

It was recently conjectured that the quantum complexity of a holographic boundary state can be computed by evaluating the gravitational action on a bulk region known as the Wheeler-DeWitt patch. We apply this complexity=action duality to evaluate the `complexity of formation' (arXiv:1509.07876, arXiv:1512.04993), i.e., the additional complexity arising in preparing the entangled thermofield double state with two copies of the boundary CFT compared to preparing the individual vacuum states of the two copies. We find that for boundary dimensions $d>2$, the difference in the complexities grows linearly with the thermal entropy at high temperatures. For the special case $d=2$, the complexity of formation is a fixed constant, independent of the temperature. We compare these results to those found using the complexity=volume duality.

37+32 pages, 24 figures; v2 - added appendix (Insights from MERA), added references, corrected typos

References in corpus (12)

• Towards a derivation of holographic entanglement entropy
• A class of quantum many-body states that can be efficiently simulated
• Complexity and Shock Wave Geometries
• Holographic c-theorems in arbitrary dimensions
• Quantum Computation as Geometry
• Chaos and complexity by design
• Gravitational action with null boundaries
• Noether charge, black hole volume, and complexity
• Complexity Growth for AdS Black Holes
• On Volumes of Subregions in Holography and Complexity
• Switchbacks and the Bridge to Nowhere
• A geometric approach to quantum circuit lower bounds

Cited by in corpus (202)

• Chaos and complexity by design
• Circuit complexity in quantum field theory
• Towards Complexity for Quantum Field Theory States
• Comments on Holographic Complexity
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On the Time Dependence of Holographic Complexity
• Complexity and entanglement for thermofield double states
• Quantum Computation as Gravity
• Circuit complexity for free fermions
• Circuit complexity in interacting QFTs and RG flows
• Holographic Complexity in Vaidya Spacetimes II
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Circuit Complexity for Coherent States
• Subsystem Complexity and Holography
• Time Evolution of Complexity: A Critique of Three Methods
• Models of quantum complexity growth
• Holographic Complexity in Vaidya Spacetimes I
• Holographic tensor network models and quantum error correction: A topical review
• Complexity of Mixed States in QFT and Holography
• Holographic Complexity of Einstein-Maxwell-Dilaton Gravity
• Holographic complexity is nonlocal
• Holographic Complexity Equals Which Action?
• The First Law of Complexity
• On Complexity for Higher Derivative Gravities
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Time Evolution of Complexity in Abelian Gauge Theories - And Playing Quantum Othello Game -
• Quantum Information in Holographic Duality
• The effect of Dilaton on the holographic complexity growth
• A Complexity for Quantum Field Theory States and Application in Thermofield Double States
• Complexity for Conformal Field Theories in General Dimensions
• Renormalized Circuit Complexity
• Complexity Growth Rate in Lovelock Gravity
• Evolution of Complexity Following a Global Quench
• Cosmological Complexity
• Action growth of charged black holes with a single horizon
• Holographic Complexity for Defects Distinguishes Action from Volume
• Principles and symmetries of complexity in quantum field theory
• Subregion Action and Complexity
• Uncharged and charged anisotropic like--Durgapal stellar model with vanishing complexity
• Krylov complexity in quantum field theory, and beyond
• Complexity growth rates for AdS black holes in massive gravity and $f(R)$ gravity
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Surface Counterterms and Regularized Holographic Complexity
• Complexity of the AdS Soliton
• Entangling power and quantum circuit complexity
• Holographic Complexity and Volume
• Evolution of complexity following a quantum quench in free field theory
• Holographic Complexity and de Sitter Space
• Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
• 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
• Path Integral Optimization for $T\bar{T}$ Deformation
• Holographic Complexity and Two Identities of Action Growth
• Action growth rate for a higher curvature gravitational theory
• Testing Holographic Conjectures of Complexity with Born-Infeld Black Holes
• Connecting Fisher information to bulk entanglement in holography
• A complexity/fidelity susceptibility g-theorem for AdS${}_3$/BCFT${}_2$
• Circuit Complexity From Cosmological Islands
• Complexity of Holographic Superconductors
• Holographic local quench and effective complexity
• Holographic Complexity in dS${}_{d+1}$
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Circuit Complexity for Fermionic Thermofield Double states
• Complexity and action for warped AdS black holes
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Complexity in the presence of a boundary
• Holographic Complexity of Quantum Black Holes
• Holographic complexity of anisotropic black branes
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
• Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
• Time evolution of the complexity in chaotic systems: concrete examples
• More on complexity of operators in quantum field theory
• Circuit complexity for generalised coherent states in thermal field dynamics
• Trans-IR Flows to Black Hole Singularities
• On the Noether charge and the gravity duals of quantum complexity
• Holographic Complexity Growth Rate in Horndeski Theory
• Interior Structure and Complexity Growth Rate of Holographic Superconductor from M-Theory
• Holographic Subregion Complexity for Singular Surfaces
• Thoughts on Holographic Complexity and its Basis-dependence
• Exact Gravity Duals for Simple Quantum Circuits
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• General Bounds on Holographic Complexity
• Complexity=Anything: Singularity Probes
• Complexity of AdS_5 black holes with a rotating string
• Holographic Path-Integral Optimization
• Computational complexity of the landscape II - Cosmological considerations
• Nonanalyticity of circuit complexity across topological phase transitions
• On Complexity Growth in Minimal Massive 3D Gravity
• Volume and complexity for warped AdS black holes
• Complexity and phase transitions in a holographic QCD model
• The Cosmological Switchback Effect
• Charged Complexity and the Thermofield Double State
• Mixed State Entanglement for Holographic Axion Model
• Comparison of holographic and field theoretic complexities by time dependent thermofield double states
• Lovelock action with nonsmooth boundaries
• Holographic Subregion Complexity in Einstein-Born-Infeld theory
• Complexity/Action duality of shock wave geometry in a massive gravity theory
• Is Action Complexity better for de Sitter space in Jackiw-Teitelboim gravity?
• On volume subregion complexity in Vaidya spacetime
• Holographic Complexity and Charged Scalar Fields
• Complexity growth of rotating black holes with a probe string
• Holographic complexity and thermodynamics of AdS black holes
• Investigating two counting methods of the holographic complexity
• Entanglement Entropy and Subregion Complexity in Thermal Perturbations around Pure-AdS Spacetime
• Modified "complexity equals action" conjecture
• Holographic complexity in charged Vaidya black hole
• On the Role of Counterterms in Holographic Complexity
• On subregion action complexity in AdS${}_3$ and in the BTZ black hole
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Volume complexity for Janus ${\mathrm{AdS}}_3$ geometries
• Holographic complexity of local quench at finite temperature
• Terminal Holographic Complexity
• Volume complexity of dS bubbles
• Regularizations of Action-Complexity for a Pure BTZ Black Hole Microstate
• Null boundary terms for Lanczos-Lovelock gravity
• Evolution of Holographic Complexity Near Critical Point
• Complexity of operators generated by quantum mechanical Hamiltonians
• Subsystem complexity in warped AdS
• Action complexity in the presence of defects and boundaries
• Mixed State Entanglement and Thermal Phase Transitions
• Time dependence of complexity for Lovelock black holes
• Complexity-action of subregions with corners
• Holographic complexity of charged Taub-NUT-AdS black holes
• Complexity Growth in Flat Spacetimes
• Holographic subregion complexity of boosted black brane and Fisher information
• Chemistry and Complexity for Solitons in AdS${}_5$
• Revisit on holographic complexity in two-dimensional gravity
• Holographic complexity for black branes with momentum relaxation
• Holographic complexity of Jackiw-Teitelboim gravity from Karch-Randall braneworld
• Generalized Volume-Complexity For Two-Sided Hyperscaling Violating Black Branes
• Holographic complexity of the electromagnetic black hole
• Volume complexity for the non-supersymmetric Janus AdS${}_5$ geometry
• Topological and Time Dependence of the Action-Complexity Relation
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Decoherence and Microscopic Diffusion at SYK
• Complexity and Multi-boundary Wormholes
• Primordial Gravitational Wave Circuit Complexity
• Comments on Joint Terms in Gravitational Action
• Complexity growth in Gubser-Rocha models with momentum relaxation
• Subregion complexity in holographic thermalization with dS boundary
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Holographic complexity in general quadratic curvature theory of gravity
• Bending the Bruhat-Tits Tree II: the p-adic BTZ Black hole and Local Diffeomorphism on the Bruhat-Tits Tree
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• The Cosmological Switchback Effect II
• On Volume Subregion Complexity in Non-Conformal Theories
• Quantum complexity and the virial theorem
• Complexity growth of massive black hole with a probe string
• Subregion complexity and confinement-deconfinement transition in a holographic QCD model
• To be unitary-invariant or not?: a simple but non-trivial proposal for the complexity between states in quantum mechanics/field theory
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Reparameterization Dependence is Useful for Holographic Complexity
• Action complexity of charged black holes with higher derivative interactions
• Holographic complexity of rotating black holes with conical deficits
• Complexity, scaling, and a phase transition
• Holographic Complexity in a Charged Supersymmetric Black Holes
• Holographic Complexity and Phase Transition for AdS Black Holes
• Negative Complexity of Formation: the Compact Dimensions Strike Back
• Quantum complexity phase transitions in monitored random circuits
• Complexity growth for topological black holes by holographic method
• Holographic complexity under a global quantum quench
• Effects of the acceleration on holographic complexity
• Weighting gates in circuit complexity and holography
• Generalized holographic complexity of rotating black holes
• Entanglement renormalization of thermofield double states
• Complexity growth of BTZ black hole in massive gravity with a null string
• Holographic information theoretic quantities for Lifshitz black hole
• Towards a Fisher-information description of complexity in de Sitter universe
• Holographic complexity for nonlinearly charged Lifshitz black holes
• More on Holographic Volumes, Entanglement, and Complexity
• The Complexity of Being Entangled
• Perturbative Complexity of Interacting Theory
• Causality Constraint on Circuit Complexity from $COSMOEFT$
• On Complexity of Holographic Flavors
• Insensitivity of the complexity rate of change to the conformal anomaly and Lloyd's bound as a possible renormalization condition
• Complexity Conjecture of Regular Electric Black Holes
• Holographic entanglement entropy and complexity of microstate geometries
• Non-analyticity in Holographic Complexity near Critical points
• Quantum fluctuation on the worldsheet of probe string in BTZ black hole
• Subsystem Complexity and Measurements in Holography
• Holographic non-computers
• What kind of "complexity" is dual to holographic complexity?
• Complexity Growth of Dyonic Black holes with Quartic Field Strength Corrections
• Operator Approach to Complexity : Excited States
• D5-brane on topological black holes
• Holographic complexity of rotating black holes
• Holographic complexity of the Klebanov-Strassler background
• Holographic and QFT Complexity with angular momentum
• Complexity, chaos and the moving D3-brane
• Geometry of quantum complexity
• Complexity of Magnetization and Magnetic Simplification
• Switchback effect of holographic complexity in multiple-horizon black holes
• Entanglement Entropy and Complexity in Dyonic Quantum Black Holes
• Finite complexity of the de Sitter vacuum
• Probe strings on AdS accelerating black holes
• Cost of holographic path integrals
• Circuit Complexity for Coherent-Thermal States in Bosonic String Theory
• Holographic timelike entanglement and subregion complexity with scalar hair
• Developments in non-relativistic field theory and complexity
• D5-brane in AdS black holes with nonzero gauge flux