A class of quantum many-body states that can be efficiently simulated

Abstract

We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive causal structure, the MERA allows for an exact evaluation of local expectation values. It is also the structure underlying entanglement renormalization, a coarse-graining scheme for quantum systems on a lattice that is focused on preserving entanglement.

4 pages, 5 figures

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• Note on surface growth approach for bulk reconstruction
• Entanglement renormalization for gauge invariant quantum fields
• Scale Invariant Entanglement Negativity at the Many-Body Localization Transition
• Matrix Product States with adaptive global symmetries
• Quantum Compression of Tensor Network States
• Inverse problem of correlation functions in holography
• Capturing long-range memory structures with tree-geometry process tensors
• Information Graph Flow: a geometric approximation of quantum and statistical systems
• Towards Holographic Quantum Energy Teleportation
• Classification of topological symmetry sectors on anyon rings
• From entanglement renormalisation to the disentanglement of quantum double models
• Tensor renormalization group approach to classical dimer models
• Uniform Matrix Product State in the Thermodynamic Limit
• Two-dimensional local Hamiltonian problem with area laws is QMA-complete
• Generalized mean field description of entanglement in dimerized spin systems
• Méthodes de calcul avec réseaux de tenseurs en physique (Basic tensor network computations in physics)
• Bosonic entanglement renormalization circuits from wavelet theory
• Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains
• TNSPackage: A Fortran2003 library designed for tensor network state methods
• Combination of Tensor Network States and Green's function Monte Carlo
• Quantum Rényi entropy by optimal thermodynamic integration paths
• Topological Defects in Quantum Field Theory with Matrix Product States
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Efficient Quantum Circuits based on the Quantum Natural Gradient
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• The Kibble Zurek Mechanism of Topological Defect Formation in Quantum Field Theory with Matrix Product States
• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Emergent geometry and path integral optimization for a Lifshitz action
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Low-temperature Gibbs states with tensor networks
• Weighting gates in circuit complexity and holography
• Holographic Interpretation of Shannon Entropy of Coherence of Quantum Pure States
• Fermionic tensor network contraction for arbitrary geometries
• Universal edge information from wave-function deformation
• Variational quantum simulation of critical Ising model with symmetry averaging
• Quantum Decimation in Hilbert Space: Coarse-Graining without Structure
• Tensor networks and efficient descriptions of classical data
• Simulation of Anyons Using Symmetric Tensor Network Algorithms
• Renormalization view on resonance proliferation between many-body localized phases
• A polynomial-time algorithm for ground states of spin trees
• Spin-spin correlations between two Kondo impurities coupled to an open Hubbard chain
• Numerical continuum tensor networks in two dimensions
• Towards a Fisher-information description of complexity in de Sitter universe
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
• Permutation-equivariant quantum convolutional neural networks
• Emergent geometry, thermal CFT and surface/state correspondence
• Localization renormalization and quantum Hall systems
• The Future of the Correlated Electron Problem
• Practical variational tomography for critical 1D systems
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Physical consequences of P$\ne$NP and the DMRG-annealing conjecture
• Machine learning, quantum chaos, and pseudorandom evolution
• Tensor network non-zero testing
• Time Evolution and Deterministic Optimisation of Correlator Product States
• Entanglement renormalization for chiral topological phases
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Quantum measurement in two-dimensional conformal field theories: Application to quantum energy teleportation
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions
• Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Renormalization of lattice field theories with infinite-range wavelets
• One-half reflected entropy is not a lower bound for entanglement of purification
• Loop update for infinite projected entangled-pair states in two spatial dimensions
• Simulation of Quantum Many-Body Systems on Amazon Cloud
• Entanglement compression in scale space: from the multiscale entanglement renormalization ansatz to matrix product operators
• Operator-algebraic renormalization and wavelets
• A new perspective to formulate a dissipative thermo field dynamics
• TensorKrowch: Smooth integration of tensor networks in machine learning
• Overlapping qubits from non-isometric maps and de Sitter tensor networks
• The Autodidactic Universe
• Quantum Gauge Networks: A New Kind of Tensor Network
• Simulation of quantum physics with Tensor Processing Units: brute-force computation of ground states and time evolution
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Simulating Quantum Turbulence with Matrix Product States
• Quantum circuit complexity and unsupervised machine learning of topological order
• Efficient Electronic Structure Theory via Hierarchical Scale-Adaptive Coupled-Cluster Formalism: I. Theory and Computational Complexity Analysis
• Adiabatic ground state preparation in an expanding lattice
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Entanglement renormalization of anisotropic XY model
• Celestial Quantum Error Correction II: From Qudits to Celestial CFT
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Zero-site DMRG and the optimal low-rank correction
• Simulation of the Ring-exchange Models with Projected Entangled Pair States
• Incommensurate Matrix Product State for Quantum Spin Systems
• Holographic Classical Shadow Tomography
• On Infinite Tensor Networks, Complementary Recovery and Type II Factors
• Implementing the sine transform of fermionic modes as a tensor network
• A tensor network representation of path integrals: Implementation and analysis
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Multilayer wave functions: A recursive coupling of local excitations
• Quantum data generation in a denoising model with multiscale entanglement renormalization network
• Efficient 2D Tensor Network Simulation of Quantum Systems
• Entanglement renormalization and symmetry fractionalization
• Entanglement across scales: Quantics tensor trains as a natural framework for renormalization
• The Software Landscape for the Density Matrix Renormalization Group
• MERACLE: Constructive layer-wise conversion of a Tensor Train into a MERA
• Quantum Entanglement of Tensor Networks with Symmetry Projections
• Anomalies of global symmetries on the lattice
• Entanglement renormalization for quantum fields with boundaries and defects
• Build your own tensor network library: DMRjulia I. Basic library for the density matrix renormalization group
• Fast Tensor Disentangling Algorithm
• Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model
• Approximate recovery with locality and symmetry constraints
• On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain
• GuiTeNet: A graphical user interface for tensor networks
• Qubit recycling and the path counting problem
• Implicitly disentangled renormalization
• Holographic Tensor Networks as Tessellations of Geometry
• Holographic Code Rate
• Explaining Anomalies with Tensor Networks
• Mapping the Hubbard model to the t-J model using ground state unitary transformations
• Leaf-to-leaf distances in Catalan trees
• Light Cone Cancellation for Variational Quantum Eigensolver in Solving Noisy Max-Cut
• Cost of holographic path integrals
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Truncating loopy tensor networks by zero-mode gauge fixing
• Feasible Architecture for Quantum Fully Convolutional Networks
• Emulation of large-scale qubit registers with a phase-space approach
• Random Walk of Bipartite Spins in a Classicalized Holographic Tensor Network
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Holographic entanglement renormalisation for fermionic quantum matter
• Exact Mappings in Condensed Matter Physics
• Are there any Landau poles in wavelet-based quantum field theory?
• Holography of Transmission Lines: Insights of Continuous MERA and AdS/CFT
• Tensor network states for the description of quantum many-body systems