Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence

Abstract

We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed by Almheiri et. al in arXiv:1411.7041.

40 Pages + 25 Pages of Appendices. 38 figures. Typos and bibliographic amendments and minor corrections

References in corpus (8)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Black holes as mirrors: quantum information in random subsystems
• A class of quantum many-body states that can be efficiently simulated
• Causality & holographic entanglement entropy
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Fault-tolerant logical gates in quantum error-correcting codes
• Quantum Error Correction of Observables
• Framework for classifying logical operators in stabilizer codes

Cited by in corpus (557)

• The ITensor Software Library for Tensor Network Calculations
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Chaos in quantum channels
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Complexity, action, and black holes
• Emergent Gravity and the Dark Universe
• Tensor networks for complex quantum systems
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Holographic duality from random tensor networks
• Chaos and complexity by design
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Tensor Network Renormalization
• Fracton Phases of Matter
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Holographic Entanglement of Purification
• Quantum Simulation for High Energy Physics
• Quantum Supremacy and the Complexity of Random Circuit Sampling
• Emergent statistical mechanics of entanglement in random unitary circuits
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture
• Chaos, Complexity, and Random Matrices
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Entanglement Transitions from Holographic Random Tensor Networks
• Exact dynamics in dual-unitary quantum circuits
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• The Holographic Entropy Cone
• Entanglement of purification: from spin chains to holography
• Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Programmable Interactions and Emergent Geometry in an Atomic Array
• Quantum Metasurfaces
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• cMERA as Surface/State Correspondence in AdS/CFT
• Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
• Islands in cosmology
• Entanglement Wedge Cross Section from the Dual Density Matrix
• Large N algebras and generalized entropy
• Flat entanglement spectra in fixed-area states of quantum gravity
• Random access quantum information processors
• Holographic Renyi Entropy from Quantum Error Correction
• Entanglement Wedge Reconstruction via Universal Recovery Channels
• Subsystem Complexity and Holography
• Path-Integral Complexity for Perturbed CFTs
• Quantifying nonstabilizerness of matrix product states
• Entanglement, Holography and Causal Diamonds
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Constructions and Noise Threshold of Hyperbolic Surface Codes
• Crystallography of Hyperbolic Lattices
• De Sitter Holography and Entanglement Entropy
• Tensor Networks from Kinematic Space
• Holographic Complexity in Vaidya Spacetimes I
• Edge modes of gravity -- II: Corner metric and Lorentz charges
• Renormalization of tensor networks using graph independent local truncations
• Holographic tensor network models and quantum error correction: A topical review
• Entanglement Negativity at Measurement-Induced Criticality
• Bidirectional holographic codes and sub-AdS locality
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• Holographic Complexity of Einstein-Maxwell-Dilaton Gravity
• Conformal field theories are magical
• Generalized entropy for general subregions in quantum gravity
• Disentangling Scrambling and Decoherence via Quantum Teleportation
• Complexity and the bulk volume, a new York time story
• Holographic Complexity Equals Which Action?
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Entanglement Wedge Cross Sections Require Tripartite Entanglement
• Information Flow in Black Hole Evaporation
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• The First Law of Complexity
• Global symmetry, Euclidean gravity, and the black hole information problem
• Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK
• Classical Shadow Tomography with Locally Scrambled Quantum Dynamics
• Entanglement Wedge Reconstruction and Entanglement of Purification
• Entanglement of Purification for Multipartite States and its Holographic Dual
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Automorphic Bloch theorems for hyperbolic lattices
• Topological Complexity in AdS3/CFT2
• Linear-Time Maximum Likelihood Decoding of Surface Codes over the Quantum Erasure Channel
• Entanglement and quantum combinatorial designs
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• $p$-adic AdS/CFT
• Learning the Alpha-bits of Black Holes
• Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum MacWilliams identity
• Continuous symmetries and approximate quantum error correction
• Entanglement entropy and superselection sectors I. Global symmetries
• Quantum Information in Holographic Duality
• Holographic Subregion Complexity from Kinematic Space
• A modular toolkit for bulk reconstruction
• Holographic Complexity And Cosmological Singularities
• Entanglement area laws for long-range interacting systems
• Treelike interactions and fast scrambling with cold atoms
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Machine Learning Spatial Geometry from Entanglement Features
• Emergent perturbation independent decay of the Loschmidt echo in a many-spin system studied through scaled dipolar dynamics
• Complexity Growth Rate in Lovelock Gravity
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
• Multipartite Entanglement in Stabilizer Tensor Networks
• Holographic Quantum Circuits from Splitting/Joining Local Quenches
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Probing Hawking radiation through capacity of entanglement
• Quantum minimal surfaces from quantum error correction
• Symmetry-Resolved Entanglement in AdS${}_3$/CFT${}_2$ coupled to $U(1)$ Chern-Simons Theory
• From Path Integrals to Tensor Networks for AdS/CFT
• Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models
• Rigorous RG algorithms and area laws for low energy eigenstates in 1D
• Scrambling and Complexity in Phase Space
• Measuring nonstabilizerness via multifractal flatness
• Bit Threads and Holographic Monogamy
• Chern insulator in a hyperbolic lattice
• The ghost in the radiation: Robust encodings of the black hole interior
• Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains
• Symmetry-resolved entanglement for excited states and two entangling intervals in AdS${}_3$/CFT${}_2$
• Entanglement Holographic Mapping of Many-Body Localized System by Spectrum Bifurcation Renormalization Group
• Complexity Growth in Integrable and Chaotic Models
• Quantum coding with low-depth random circuits
• Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
• Holographic entanglement negativity and replica symmetry breaking
• Holographic Inequalities and Entanglement of Purification
• Multipartite entanglement in heterogeneous systems
• AdS/CFT as a deep Boltzmann machine
• Towards Bulk Metric Reconstruction from Extremal Area Variations
• Logical blocks for fault-tolerant topological quantum computation
• Thirty-six entangled officers of Euler: Quantum solution to a classically impossible problem
• Hyper-invariant tensor networks and holography
• Entanglement phase transitions in random stabilizer tensor networks
• Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Entanglement Wedge Reconstruction using the Petz Map
• Exploring the Tensor Networks/AdS Correspondence
• Classifying boundary conditions in JT gravity: from energy-branes to $\alpha$-branes
• Calderbank-Steane-Shor Holographic Quantum Error Correcting Codes
• Code properties from holographic geometries
• Higher-order topological insulators in hyperbolic lattices
• Entanglement entropy in two dimensional string theory
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Island for Gravitationally Prepared State and Pseudo Entanglement Wedge
• Non-stabilizerness versus entanglement in matrix product states
• Entanglement of Purification in Free Scalar Field Theories
• Constructing optimal quantum error correcting codes from absolute maximally entangled states
• Pulling the Boundary into the Bulk
• Machine Learning Holographic Mapping by Neural Network Renormalization Group
• Construction and the ergodicity properties of dual unitary quantum circuits
• Generalizations of Reflected Entropy and the Holographic Dual
• Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface
• Towards Entanglement of Purification for Conformal Field Theories
• Entanglement Wedges for Gravitating Regions
• Holographic spacetime, black holes and quantum error correcting codes: A review
• Entanglement Entropy and the Colored Jones Polynomial
• Finding Pythons in Unexpected Places
• One-loop universality of holographic codes
• Conformal Quasicrystals and Holography
• On Distinguishability of Black Hole Microstates
• Tensor network and ($p$-adic) AdS/CFT
• Exact holographic mapping in free fermion systems
• On the Holographic Dual of a Topological Symmetry Operator
• Rigorous free fermion entanglement renormalization from wavelet theory
• Conditional Mutual Information of Bipartite Unitaries and Scrambling
• Spacetime from Unentanglement
• New perspectives on covariant quantum error correction
• Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks
• Holographic Complexity of Quantum Black Holes
• Signature of quantum chaos in operator entanglement in 2d CFTs
• Bit threads and holographic entanglement of purification
• Continuous Tensor Network States for Quantum Fields
• Holographic measurement and bulk teleportation
• De Sitter Space as a Tensor Network: Cosmic No-Hair, Complementarity, and Complexity
• Multipartite Purification, Multiboundary Wormholes and Islands in AdS${}_3$/CFT${}_2$
• Path-Integral Optimization from Hartle-Hawking Wave Function
• Toy Models of Holographic Duality between local Hamiltonians
• Topological shadows and complexity of islands in multiboundary wormholes
• Ensemble from Coarse Graining: Reconstructing the Interior of an Evaporating Black Hole
• Quantum Codes from Neural Networks
• Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• Mixed state entanglement measures as probe for confinement
• Selberg trace formula in hyperbolic band theory
• Entanglement from Topology in Chern-Simons Theory
• Holographic coherent states from random tensor networks
• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Modular Flow as a Disentangler
• Anderson localization transition in disordered hyperbolic lattices
• Distinguishing Random and Black Hole Microstates
• Geometry and entanglement in the scattering matrix
• The physical meaning of the holographic principle
• Bulk metric reconstruction from boundary entanglement
• Information geometry in quantum field theory: lessons from simple examples
• Quantum Information Scrambling: From Holography to Quantum Simulators
• Intertwiner Entanglement on Spin Networks
• Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
• Central charges of aperiodic holographic tensor network models
• Cutoff Dependence and Complexity of the CFT${}_2$ Ground State
• Growth of entanglement of generic states under dual-unitary dynamics
• Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
• Soft mode and interior operator in Hayden-Preskill thought experiment
• Holographic Path-Integral Optimization
• Statistical mechanics model for Clifford random tensor networks and monitored quantum circuits
• Majorana dimers and holographic quantum error-correcting codes
• Entanglement structures in qubit systems
• Constructions of k-uniform and absolutely maximally entangled states beyond maximum distance codes
• Normal projected entangled pair states generating the same state
• Quantum error correction codes and absolutely maximally entangled states
• Firewalls vs. Scrambling
• Toward random tensor networks and holographic codes in CFT
• Locality from the Spectrum
• Construction and local equivalence of dual-unitary operators: from dynamical maps to quantum combinatorial designs
• Tensor-network codes
• Tensor network models of AdS/qCFT
• Limits on the storage of quantum information in a volume of space
• A defect in holographic interpretations of tensor networks
• Correlation measures and distillable entanglement in AdS/CFT
• Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength
• Horizon as Critical Phenomenon
• Quantum Max-flow/Min-cut
• The Quantum Entropy Cone of Hypergraphs
• Random tensor networks with nontrivial links
• Towards holography via quantum source-channel codes
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
• Scrambling and decoding the charged quantum information
• Geometry and Complexity of Path Integrals in Inhomogeneous CFTs
• Universal Fault-Tolerant Quantum Computing with Stabiliser Codes
• Entanglement renormalization, quantum error correction, and bulk causality
• Design and Experimental Performance of Local Entanglement Witness Operators
• Holographic complexity: A tool to probe the property of reduced fidelity susceptibility
• Geometrizing quantum dynamics of a Bose-Einstein condensate
• Holographic Complexity Of Cold Hyperbolic Black Holes
• Exploring the Membrane Theory of Entanglement Dynamics
• Circuits of space and time quantum channels
• Emergent decoherence induced by quantum chaos in a many-body system: A Loschmidt echo observation through NMR
• Deriving the PEE proposal from the Locking bit thread configuration
• Approximate Bacon-Shor Code and Holography
• Quantum stabilizer codes, lattices, and CFTs
• Topological wormholes
• An emergent geometric description for a topological phase transition in the Kitaev superconductor model
• Coarse-Graining Holographic States: A Semiclassical Flow in General Spacetimes
• Quantum Null Geometry and Gravity
• One-shot holography
• Extracting entanglement geometry from quantum states
• Emergent 4-dimensional linearized gravity from spin foam model
• Quantum gravity states, entanglement graphs and second-quantized tensor networks
• Quantum variational learning for quantum error-correcting codes
• Holographic Cone of Average Entropies
• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• Black holes as clouded mirrors: the Hayden-Preskill protocol with symmetry
• Real-space RG, error correction and Petz map
• Precursors, Gauge Invariance, and Quantum Error Correction in AdS/CFT
• Unitary Networks from the Exact Renormalization of Wave Functionals
• Tensor Network Models of Multiboundary Wormholes
• Interacting fields in real-time AdS/CFT
• CFT sewing as the dual of AdS cut-and-paste
• Absolutely maximally entangled state equivalence and the construction of infinite quantum solutions to the problem of 36 officers of Euler
• Holographic Relative Entropy in Infinite-dimensional Hilbert Spaces
• Building Tensor Networks for Holographic States
• Magic State Distillation from Entangled States
• Holographic Codes from Hyperinvariant Tensor Networks
• Emergent Einstein Equation in p-adic CFT Tensor Networks
• Tensor networks for dynamic spacetimes
• Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks
• Holographic confining/deconfining gauge theories and entanglement measures with a magnetic field
• Observer-dependent black hole interior from operator collision
• Tripartite information of highly entangled states
• Radial Cutoffs and Holographic Entanglement
• Tensor networks for quantum computing
• Entanglement, Soft Modes, and Celestial Holography
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Qubit Construction in 6D SCFTs
• Holographic description of Narain CFTs and their code-based ensembles
• Decoding Holographic Codes with an Integer Optimisation Decoder
• Gravitational back-reaction is magical
• Code subspaces for LLM geometries
• Quantum tasks in holography
• Approximate symmetries and quantum error correction
• Matrix product state renormalization
• Path Integral Complexity and Kasner singularities
• On the fate of the Hoop Conjecture in quantum gravity
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• A non-perturbative field theory approach for the Kondo effect: Emergence of an extra dimension and its implication for the holographic duality conjecture
• The entanglement membrane in exactly solvable lattice models
• Planar Maximally Entangled States
• Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays
• Bulk Reconstruction Beyond the Entanglement Wedge
• Path Integrals for Causal Diamonds and the Covariant Entropy Principle
• Tensor network representations from the geometry of entangled states
• Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
• Kinematic Space and Wormholes
• Dynamics for holographic codes
• One-shot quantum error correction of classical and quantum information
• Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
• Locally Maximally Entangled States of Multipart Quantum Systems
• Holographic maps from quantum gravity states as tensor networks
• Estimating localizable entanglement from witnesses
• Explicit reconstruction of the entanglement wedge
• Inhomogeneous quenches as state preparation in two-dimensional conformal field theories
• 9 $\times$ 4 = 6 $\times$ 6: Understanding the quantum solution to the Euler's problem of 36 officers
• Quantum Error Correction in the Black Hole Interior
• Building Bulk Geometry from the Tensor Radon Transform
• Scalable characterization of localizable entanglement in noisy topological quantum codes
• Seeing the Entanglement Wedge
• More of the Bulk from Extremal Area Variations
• Invariant Perfect Tensors
• Quantum bit threads of MERA tensor network in large $c$ limit
• Quantum Causal Influence
• A note on the AdS/CFT correspondence and the nature of spacetime in quantum gravity
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
• Tensor renormalization group in bosonic field theory
• Conformal Properties of Hyperinvariant Tensor Networks
• The minimal canonical form of a tensor network
• An algorithm to explore entanglement in small systems
• Differentiable Programming of Isometric Tensor Networks
• RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior
• Pseudo entropy under joining local quenches
• Towards a dS/MERA correspondence
• Geodesic string condensation from symmetric tensor gauge theory: a unifying framework of holographic toy models
• Benchmarking treewidth as a practical component of tensor-network--based quantum simulation
• Beyond islands: A free probabilistic approach
• Surface growth scheme for bulk reconstruction and tensor network
• Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions
• Dual Field Theories of Quantum Computation
• Holographic duality between local Hamiltonians from random tensor networks
• Holographic Tensor Networks with Bulk Gauge Symmetries
• Boundary theories of critical matchgate tensor networks
• Black holes often saturate entanglement entropy the fastest
• Markovian and non-Markovian quantum measurements
• Statistical Mechanics of Monitored Dissipative Random Circuits
• Fault-tolerant logical gates in holographic stabilizer codes are severely restricted
• The Spacetime Geometry of Fixed-Area States in Gravitational Systems
• Bulk reconstruction of metrics inside black holes by complexity
• Anyonic Defect Branes and Conformal Blocks in Twisted Equivariant Differential (TED) K-theory
• Discrete Gravity on Random Tensor Network and Holographic Rényi Entropy
• Geometrizing the Partial Entanglement Entropy: from PEE Threads to Bit Threads
• Quantum bit threads and holographic entanglement
• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• Holographic tensor networks from hyperbolic buildings
• Symmetry Resolution in non-Lorentzian Field Theories
• Holographic Reconstruction of Bubbles
• Anderson transition and mobility edges on hyperbolic lattices with randomly connected boundaries
• Wilson line networks in $p$-adic AdS/CFT
• Entanglement entropy and correlations in loop quantum gravity
• Local tensor-network codes
• Holographic spin networks from tensor network states
• Gauging the bulk: generalized gauging maps and holographic codes
• Exactly solvable many-body dynamics from space-time duality
• Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• Quantum error correction and large $N$
• Entanglement Area Law for Shallow and Deep Quantum Neural Network States
• Generalized Exact Holographic Mapping with Wavelets
• Combing gravitational hair in 2+1 dimensions
• Entanglement entropy and monotones in scattering process
• Tensor network state correspondence and holography
• Entanglement Dynamics of the Non-Unitary Holographic Channel
• The action of HRT-areas as operators in semiclassical gravity
• Holographic integral geometry with time dependence
• Diagonal unitary and orthogonal symmetries in quantum theory II: Evolution operators
• The quantum cat map on the modular discretization of extremal black hole horizons
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• Classical Spacetimes as Amplified Information in Holographic Quantum Theories
• Entanglement renormalization and integral geometry
• Bulk Locality and Entanglement Swapping in AdS/CFT
• Multipartite edge modes and tensor networks
• Python's Lunches in Jackiw-Teitelboim gravity with matter
• Eigenstate Thermalization Hypothesis and Approximate Quantum Error Correction
• Bending the Bruhat-Tits Tree I:Tensor Network and Emergent Einstein Equations
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Deconfinement and Error Thresholds in Holography
• Entanglement distillation toward minimal bond cut surface in tensor networks
• Non-Isometric Quantum Error Correction in Gravity
• The Inverse of Exact Renormalization Group Flows as Statistical Inference
• Correspondence between Entanglement Growth and Probability Distribution of Quasi-Particles
• Background independent tensor networks
• Hyperbolic lattices and two-dimensional Yang-Mills theory
• Anyons in Geometric Models of Matter
• Geometric encoding of renormalization group $\beta -$functions in an emergent holographic dual description
• On Quantum Simulation Of Cosmic Inflation
• Thread/State correspondence: from bit threads to qubit threads
• Bulk Locality and Asymptotic Causal Diamonds
• Landauer's principle in Qubit-Cavity quantum field theory Interaction in Vacuum and Thermal States
• Quantum error correction and entanglement spectrum in tensor networks
• A finite geometric toy model of space-time as an error correcting code
• Multivariate Trace Inequalities, p-Fidelity, and Universal Recovery Beyond Tracial Settings
• Certifying Quantum Separability with Adaptive Polytopes
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity
• Holographic Weak Measurement
• Algebra of Hyperbolic Band Theory under Magnetic Field
• Notes on the Causal Structure in a Tensor Network
• MERA as a holographic strange correlator
• Generalised second law beyond the semiclassical regime
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Eigenmodes of the Laplacian on Hyperbolic Lattices
• Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
• Quantum Error Correction and Holographic Information from Bilocal Holography
• Tensor network decompositions for absolutely maximally entangled states
• Holographic relations for OPE blocks in excited states
• Analytical percolation theory for topological color codes under qubit loss
• Understanding holographic error correction via unique algebras and atomic examples
• How much entanglement is needed for quantum error correction?
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Quantum Error-Detection at Low Energies
• Stabilizer Formalism for Operator Algebra Quantum Error Correction
• Tensor chain and constraints in tensor networks
• Berry curvature, horocycles and scattering states in $Ad{S}_3/CF{T}_2$
• Note on surface growth approach for bulk reconstruction
• Topological string entanglement
• Inverse problem of correlation functions in holography
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• The Quantum Gravity Disk: Discrete Current Algebra
• Properties of Modular Hamiltonians on Entanglement Plateaux
• Holographic networks for (1+1)-dimensional de Sitter spacetime
• Introduction to quantum entanglement in many-body systems
• Quantum error correction meets continuous symmetries: fundamental trade-offs and case studies
• Quantum Compression of Tensor Network States
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Tensor Network Models of Unitary Black Hole Evaporation
• Subsystem entropy in 2d CFT and KdV ETH
• Dual-isometric Projected Entangled Pair States
• Single-shot holographic compression from the area law
• Quantum geometric information flows and relativistic generalizations of G. Perelman thermodynamics for nonholonomic Einstein systems with black holes and stationary solitonic hierarchies
• Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
• Entanglement entropy and non-local duality: quantum channels and quantum algebras
• Two-Unitary Complex Hadamard Matrices of Order $36$
• Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory
• Krylov operator complexity in holographic CFTs: Smeared boundary reconstruction and the dual proper radial momentum
• Translationally-Invariant Universal Quantum Hamiltonians in 1D
• Hayden-Preskill Recovery in Hamiltonian Systems
• Construction of perfect tensors using biunimodular vectors
• Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning
• TNSPackage: A Fortran2003 library designed for tensor network state methods
• Kaluza--Klein gravity & cosmology emerging from G. Perelman's entropy functionals and quantum geometric information flows
• On the first law of entanglement for Quasi-Topological gravity
• Operator-state correspondence in simple current extended conformal field theories: Toward a general understanding of chiral conformal field theories and topological orders
• Constraining higher order gravities with subregion duality
• Distributed Encoding and Decoding of Quantum Information over Networks
• Holography without holography: How to turn inter-representational into intra-theoretical relations in AdS/CFT
• Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
• Measuring Holographic Entanglement Entropy on a Quantum Simulator
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• Soft thermodynamics of gravitational shock wave
• The resource theory of tensor networks
• Connectomes and Properties of Quantum Entanglement
• Remarks on Black Hole Complexity Puzzle
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• Bulk-boundary correspondence from hyper-invariant tensor networks
• Direct-dynamical entanglement-discord relations
• Bulk Spacetime Encoding via Boundary Ambiguities
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Code Properties of the Holographic Sierpinski Triangle
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction
• Towards bit threads in general gravitational spacetimes
• Conformal geometry from entanglement
• A construction of Combinatorial NLTS
• Approximate Quantum Codes From Long Wormholes
• Holographic Foliations: Self-Similar Quasicrystals from Hyperbolic Honeycombs
• Localizing genuine multiparty entanglement in noisy stabilizer states
• Counting atypical black hole microstates from entanglement wedges
• Random Invariant Tensors
• Causal Density Matrices
• Exact renormalization group for wave functionals
• Engineering holography with stabilizer graph codes
• Multiparticle singlet states cannot be maximally entangled for the bipartitions
• The area operator and fixed area states in conformal field theories
• The Holographic Map of an Evaporating Black Hole
• Classical Holographic Codes
• Tensor Renormalization Group for interacting quantum fields
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory
• Entropy production and correlation spreading in the interaction between particle detector and thermal baths
• Null wave front as Ryu-Takayanagi surface
• Quantum Holographic Entanglement Entropy to All Orders in $1/N$ Expansion
• Reconstruction wedges in $AdS/CFT$ with boundary fractallike structures
• Off-diagonal cosmological solutions in emergent gravity theories and Grigory Perelman entropy for geometric flows
• No invariant perfect qubit codes
• Decoding general error correcting codes and the role of complementarity
• Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism
• Fundamental thresholds for computational and erasure errors via the coherent information
• Solvable Quantum Circuits in Tree+1 Dimensions
• Holographic geometry/real-space entanglement correspondence and metric reconstruction
• Emergent Dark Gravity from (Non)Holographic Screens
• Higher-dimensional Fermiology in bulk moiré metals
• Puzzles and pitfalls involving Haar-typicality in holography
• Warping Wormholes with Dust: a Metric Construction of the Python's Lunch
• Weaving the (AdS) spaces with partial entanglement entropy threads
• Butterfly Velocities for Holographic Theories of General Spacetimes
• Noisy Quantum Trees: Infinite Protection Without Correction
• Phase Transitions of Correlations in Black Hole Geometries
• Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields
• Geometric Surprises in the Python's Lunch Conjecture
• Discrete Bulk Reconstruction
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT
• Entanglement Rényi entropies in celestial holography
• The Foliage Partition: An Easy-to-Compute LC-Invariant for Graph States
• Exact bosonic Matrix Product States (and holography)
• Non-stabilizerness and entanglement from cat-state injection
• Measurement-invisible quantum correlations in scrambling dynamics
• Subsystem Complexity and Measurements in Holography
• Quantum convolutional channels and multiparameter families of 2-unitary matrices
• Holographic Classical Shadow Tomography
• Cryptographic tests of the python's lunch conjecture
• Shrinking of Operators in Quantum Error Correction and AdS/CFT
• Universal graph representation of stabilizer codes
• Does connected wedge imply distillable entanglement?
• Holographic phenomenology via overlapping degrees of freedom
• Security of quantum position-verification limits Hamiltonian simulation via holography
• Towards holography for quantum mechanics
• A polynomial time algorithm for studying physical observables in chaotic eigenstates
• Revisiting holographic codes with fractal-like boundary erasures
• Black hole as a multipartite entangler: multi-entropy in AdS${}_3$/CFT${}_2$
• Toward Holography on Biregular Trees
• Quantum max-flow in the bridge graph
• Entangled universes
• Quantum Circuits for High-Dimensional Absolutely Maximally Entangled States
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Entanglement in simple spin networks with a boundary
• Holographic tensor network for double-scaled SYK
• Inspecting non-perturbative contributions to the Entanglement Entropy via wavefunctions
• Exploring uberholography
• Holographic Screen Sequestration
• Universal Entanglement and an Information-Complete Quantum Theory
• Tessellation codes: encoded quantum gates by geometric rotation
• Pseudoentanglement from tensor networks
• Celestial Quantum Error Correction I: Qubits from Noncommutative Klein Space
• Scanning space-time with patterns of entanglement
• Geometric methods in quantum information and entanglement variational principle
• Flat-space Quantum Gravity in AdS/CFT
• Growth of a renormalized operator as a probe of chaos
• A Loop Quantum Gravity Inspired Action for the Bosonic String and Emergent Dimensions at Large Scales
• Editorial: New Frontiers in Holographic Duality -- From quantum complexity and black holes to hydrodynamics and neutron stars
• Local density matrices of many-body states in the constant weight subspaces
• Searching for emergent spacetime in spin glasses
• Wire Codes
• Biased-Noise Thresholds of Zero-Rate Holographic Codes with Tensor-Network Decoding
• Explicit decoders using fixed-point amplitude amplification based on QSVT
• Hofstadter's Butterfly in AdS${}_3$ Black Holes
• Tenfold Way for Holography : AdS/CFT and Beyond
• Which entropy for general physical theories?
• Quantum Error Correction Codes for Truncated SU(2) Lattice Gauge Theories
• $\chi$-Colorable Graph States: Closed-Form Expressions and Quantum Orthogonal Arrays
• Cosmological constant as quantum error correction from generalised gauge invariance in double field theory
• Critical spin models from holographic disorder
• A graph-based approach to entanglement entropy of quantum error correcting codes
• Approximate Quantum Error Correction with 1D Log-Depth Circuits
• Scalable and fault-tolerant preparation of encoded k-uniform states
• Pseudoentanglement Ain't Cheap
• Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors
• Entanglement Suppression Due to Black Hole Scattering
• Tri-unitary quantum circuits
• Holographic Tensor Networks as Tessellations of Geometry
• Holographic AME states in black hole interiors
• Absolutely maximally entangled pure states of multipartite quantum systems
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Engineering entanglement geometry via spacetime-modulated measurements
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• More global randomness from less-random local gates