Matrix product states represent ground states faithfully

Abstract

We quantify how well matrix product states approximate exact ground states of 1-D quantum spin systems as a function of the number of spins and the entropy of blocks of spins. We also investigate the convex set of local reduced density operators of translational invariant systems. The results give a theoretical justification for the high accuracy of renormalization group algorithms, and justifies their use even in the case of critical systems.

References in corpus (6)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• DMRG and periodic boundary conditions: a quantum information perspective
• Randomizing quantum states: Constructions and applications
• Valence Bond Solids for Quantum Computation
• Is Entanglement Monogamous?
• Energy as an Entanglement Witness for Quantum Many-Body Systems

Cited by in corpus (271)

• The density-matrix renormalization group in the age of matrix product states
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum trajectories and open many-body quantum systems
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Criticality, the area law, and the computational power of PEPS
• Entropy scaling and simulability by Matrix Product States
• New Trends in Density Matrix Renormalization
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Continuous Matrix Product States for Quantum Fields
• Entanglement entropy for the long range Ising chain
• String order and symmetries in quantum spin lattices
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• N-representability is QMA-complete
• What is an integrable quench?
• General entanglement scaling laws from time evolution
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Matrix Product States for dynamical simulation of infinite chains
• Entropy and Entanglement in Quantum Ground States
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Time evolution algorithms for Matrix Product States and DMRG
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Finite automata for caching in matrix product algorithms
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Quantifying nonstabilizerness of matrix product states
• Many-body localisation implies that eigenvectors are matrix-product states
• Operator Space Entanglement Entropy in XY Spin Chains
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Long-range entanglement from measuring symmetry-protected topological phases
• Symmetry Protected Topological Order in Open Quantum Systems
• Holographic tensor network models and quantum error correction: A topical review
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Classical simulation versus universality in measurement based quantum computation
• Matrix Product State applications for the ALPS project
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Preparation of matrix product states with log-depth quantum circuits
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Fundamentals of universality in one-way quantum computation
• Concurrence and a proper monogamy inequality for arbitrary quantum states
• Tensor operators: constructions and applications for long-range interaction systems
• Measurements conspire nonlocally to restructure critical quantum states
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Holographic quantum states
• Does provable absence of barren plateaus imply classical simulability?
• Transfer Matrices and Excitations with Matrix Product States
• Universal tripartite entanglement in one-dimensional many-body systems
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Conformal Boundary Conditions of Symmetry-Enriched Quantum Critical Spin Chains
• Entanglement, combinatorics and finite-size effects in spin-chains
• Unifying variational methods for simulating quantum many-body systems
• Probing the stability of the spin liquid phases in the Kitaev-Heisenberg model using tensor network algorithms
• Designing spin-1 lattice models using polar molecules
• Computations in Quantum Tensor Networks
• Entanglement and Many-Body effects in Collective Neutrino Oscillations
• Mott-insulator phases of non-locally coupled 1D dipolar Bose gases
• Entanglement Barriers in Dual-Unitary Circuits
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Transport properties of the one-dimensional Hubbard model at finite temperature
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Sequential generation of projected entangled-pair states
• Dynamical simulation of integrable and non-integrable models in the Heisenberg picture
• Area law and vacuum reordering in harmonic networks
• Symmetry protection of measurement-based quantum computation in ground states
• Classical algorithm for simulating experimental Gaussian boson sampling
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Adiabatic Spectroscopy and a Variational Quantum Adiabatic Algorithm
• Spin and thermal conductivity of quantum spin ladders
• Multigrid Algorithms for Tensor Network States
• Dynamical simulations of classical stochastic systems using matrix product states
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• Temporal Entanglement in Chaotic Quantum Circuits
• Regional versus Global Entanglement in Resonating-Valence-Bond states
• Fractional revivals through Rényi uncertainty relations
• Generalized entanglement as a framework for complex quantum systems: Purity vs delocalization measures
• Time evolution of projected entangled pair states in the single layer picture
• Universal entanglement spectrum in gapless symmetry protected topological states
• A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• State space truncation with quantified errors for accurate solutions to discrete Chemical Master Equation
• Assessing the accuracy of projected entangled-pair states on infinite lattices
• Anyonic entanglement renormalization
• MERA for Spin Chains with Continuously Varying Criticality
• Sublinear scaling in non-Markovian open quantum systems simulations
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Scaling of neural-network quantum states for time evolution
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Quantum many-body systems in thermal equilibrium
• Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• A universal formula for the entanglement asymmetry of matrix product states
• Variational methods for contracting projected entangled-pair states
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Symmetry breaking and criticality in tensor-product states
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• The matrix product representations for all valence bond states
• Survival of entanglement in thermal states
• Variational autoencoder reconstruction of complex many-body physics
• Hubbard-to-Heisenberg crossover (and efficient computation) of Drude weights at low temperatures
• Holographic quantum simulation of entanglement renormalization circuits
• Quantum Phase Transitions and Matrix Product States in Spin Ladders
• Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss
• Renormalization algorithm with graph enhancement
• Tensor renormalization group study of the 3d $O(2)$ model
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Entanglement in highly symmetric multipartite quantum states
• Computable Rényi mutual information: Area laws and correlations
• Entanglement, fractional magnetization and long-range interactions
• Magic Resources of the Heisenberg Picture
• Symmetry Breaking and Convex Set Phase Diagrams for the q-state Potts Model
• Measuring incompatibility and clustering quantum observables with a quantum switch
• Area law in one dimension: Degenerate ground states and Renyi entanglement entropy
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• One-dimensional quantum systems at finite temperatures can be simulated efficiently on classical computers
• Enhanced TEMPO algorithm for quantum path integrals with off-diagonal system-bath coupling: applications to photonic quantum networks
• Entanglement in the quantum Ising model
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• Fermionic tensor network methods
• Dequantizing quantum machine learning models using tensor networks
• The Complexity of the Consistency and N-representability Problems for Quantum States
• Tensor networks for quantum computing
• The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
• Propagation of Many-body Localization in an Anderson Insulator
• Typical Correlation Length of Sequentially Generated Tensor Network States
• Information-entropic measures for non-zero l states of confined hydrogen-like ions
• Non-stabilizerness in kinetically-constrained Rydberg atom arrays
• Can neural quantum states learn volume-law ground states?
• Quantum State Tomography for Matrix Product Density Operators
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Computing energy density in one dimension
• Detecting Quantum Anomalies in Open Systems
• Entanglement Diagnostics for Efficient Quantum Computation
• On the closedness and geometry of tensor network state sets
• Exploiting Matrix Symmetries and Physical Symmetries in Matrix Product States and Tensor Trains
• The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks
• Ultraslow Growth of Number Entropy in an l-bit Model of Many-Body Localization
• Many-body entropies and entanglement from polynomially-many local measurements
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• Entanglement scaling in fermion chains with a localization-delocalization transition and inhomogeneous modulations
• A brief introduction to multipartite entanglement
• Evaluation of ground state entanglement in spin systems with the random phase approximation
• Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States
• Boundary theories of critical matchgate tensor networks
• Polynomial scaling enhancement in ground-state preparation of Ising spin models via counter-diabatic driving
• Deterministic generation of photonic entangled states using decoherence-free subspaces
• Non-equilibrium thermal transport and vacuum expansion in the Hubbard model
• Functional Tensor Network Solving Many-body Schrödinger Equation
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
• Entropy Constraints for Ground Energy Optimization
• Entanglement area law violation from field-curvature coupling
• Entanglement and the density matrix renormalisation group in the generalised Landau paradigm
• Localization of a mobile impurity interacting with an Anderson insulator
• Bridging Entanglement and Magic Resources within Operator Space
• Exact dimer ground states for a continuous family of quantum spin chains
• Nonequilibrium critical dynamics in the quantum chiral clock model
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Hybrid Tree Tensor Networks for quantum simulation
• Identifying quantum phases from injectivity of symmetric matrix product states
• Partonic distribution functions and amplitudes using tensor network methods
• Exact projected entangled pair ground states with topological Euler invariant
• Locally purified density operators for noisy quantum circuits
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Explainable Natural Language Processing with Matrix Product States
• Matrix Product Belief Propagation for reweighted stochastic dynamics over graphs
• Definitions of entanglement entropy of spin systems in the valence-bond basis
• Performance of the low-rank tensor-train SVD (TT-SVD) for large dense tensors on modern multi-core CPUs
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Information-Entropic Measures in Confined Isotropic Harmonic Oscillator
• Entanglement entropy scaling of noisy random quantum circuits in two dimensions
• Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit
• Exploring Shallow-Depth Boson Sampling: Towards Scalable Quantum Supremacy
• Many-body localization proximity effect in two-species bosonic Hubbard model
• Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Introduction to quantum entanglement in many-body systems
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems
• Matrix Product State representation for Slater Determinants and Configuration Interaction States
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Generalized mean field description of entanglement in dimerized spin systems
• Quantum complexity phase transitions in monitored random circuits
• An Exact Link between Nonlocal Nonstabilizerness and Operator Entanglement
• Simplicity of mean-field theories in neural quantum states
• Dual-isometric Projected Entangled Pair States
• Entanglement Measures in a Nonequilibrium Steady State: Exact Results in One Dimension
• Density matrix renormalization on random graphs and the quantum spin-glass transition
• A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation
• Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
• Inference from Matrix Products: A Heuristic Spin Glass Algorithm
• Matrix-product unitaries: Beyond quantum cellular automata
• Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries
• Entanglement Continuous Unitary Transformations
• Plaquette-type valence bond solid state in the $J_1$-$J_2$ square-lattice Heisenberg model
• Thermal Area Law for Lattice Bosons
• Large-scale stochastic simulation of open quantum systems
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• A Matrix Product State Model for Simultaneous Classification and Generation
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Information theoretic measures on quantum droplets in ultracold atomic systems
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
• Practical variational tomography for critical 1D systems
• Tensor networks and efficient descriptions of classical data
• Deconfined criticality as intrinsically gapless topological state in one dimension
• The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition
• Quantum annealing in the NISQ era: railway conflict management
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Finding maximal quantum resources
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• Many-body quantum catalysts for transforming between phases of matter
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Exploring nontrivial topology at quantum criticality in a superconducting processor
• Finding entries of maximum absolute value in low-rank tensors
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Discovering Local Hidden-Variable Models for Arbitrary Multipartite Entangled States and Arbitrary Measurements
• Understanding and utilizing the inner bonds of process tensors
• Quantum wavefunction annealing of spin glasses
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Chemical master equation parameter exploration using DMRG
• A Classifying Space for Phases of Matrix Product States
• Entanglement Renormalization of the class of Continuous Matrix Product States
• A quantum inspired approach to learning dynamical laws from data -- block-sparsity and gauge-mediated weight sharing
• Fermi surfaces of composite fermions
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
• Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
• One-dimensional symmetric phases protected by frieze symmetries
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Classification of matrix product ground states corresponding to one dimensional chains of two state sites of nearest neighbor interactions
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Reductions in finite-dimensional quantum mechanics: from symmetries to operator algebras and beyond
• Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• On the set of reduced states of translation invariant, infinite quantum systems
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling
• Generating Generalised Ground-State Ansatzes from Few-Body Examples
• Block Lanczos method for excited states on a quantum computer
• Entanglement renormalization and symmetry fractionalization
• Efficiency of neural-network state representations of one-dimensional quantum spin systems
• Deviation from maximal entanglement for mid-spectrum eigenstates of local Hamiltonians
• Les Houches Lecture Notes on Tensor Networks
• Gaussian matrix product states cannot efficiently describe critical systems
• Uncertainty relations and joint numerical ranges
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States
• On the Ordering of Sites in the Density Matrix Renormalization Group using Quantum Mutual Information
• Variational Tensor Network Simulation of Gaussian Boson Sampling and Beyond
• Non-Markovian steady states of a driven two-level system
• Emulation of large-scale qubit registers with a phase-space approach
• Using matrix-product states for time-series machine learning
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
• High-expressibility Quantum Neural Networks using only classical resources
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach
• Mutual information in interacting spin systems
• Energy Spectra of Compressed Quantum States
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Bundled matrix product states represent low-energy excitations faithfully
• Quantum Machine Learning for State Tomography Using Classical Data
• Explaining Anomalies with Tensor Networks
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Quantum Circuits for Matrix-Product Unitaries
• Quantum entropy thermalization
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Entanglement Complexity in Many-body Systems from Positivity Scaling Laws
• Continuous matrix product operators for quantum fields
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• Information analysis in free and confined harmonic oscillator
• The product structure of MPS-under-permutations