Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems

Abstract

The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how matrix product states and projected entangled pair states describe many-body wavefunctions in terms of local tensors. These tensors express how the entanglement is routed, act as a novel type of non-local order parameter, and we describe how their symmetries are reflections of the global entanglement patterns in the full system. We will discuss how tensor networks enable the construction of real-space renormalization group flows and fixed points, and examine the entanglement structure of states exhibiting topological quantum order. Finally, we provide a summary of the mathematical results of matrix product states and projected entangled pair states, highlighting the fundamental theorem of matrix product vectors and its applications.

Review article. 72 pages

References in corpus (277)

• Quantum entanglement
• Fault-tolerant quantum computation by anyons
• The Large N Limit of Superconformal Field Theories and Supergravity
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Concentrating Partial Entanglement by Local Operations
• Area laws for the entanglement entropy - a review
• Machine learning and the physical sciences
• Topological entanglement entropy
• Many body localization and thermalization in quantum statistical mechanics
• Efficient classical simulation of slightly entangled quantum computations
• Detecting topological order in a ground state wave function
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Geometric and Renormalized Entropy in Conformal Field Theory
• Topological quantum memory
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Real time evolution using the density matrix renormalization group
• Quantum Error Correction for Quantum Memories
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• An Area Law for One Dimensional Quantum Systems
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Zoo of quantum-topological phases of matter
• A class of quantum many-body states that can be efficiently simulated
• Time-dependent variational principle for quantum lattices
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Unifying time evolution and optimization with matrix product states
• Classifying quantum phases using Matrix Product States and PEPS
• Matrix product states represent ground states faithfully
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Area laws in quantum systems: mutual information and correlations
• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Efficient quantum state tomography
• Lieb-Schultz-Mattis in Higher Dimensions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• On Many-Body Localization for Quantum Spin Chains
• Tensor renormalization group approach to 2D classical lattice models
• DMRG and periodic boundary conditions: a quantum information perspective
• Criticality, the area law, and the computational power of PEPS
• Spectral Gap and Exponential Decay of Correlations
• Classical simulation of quantum many-body systems with a tree tensor network
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Area laws in a many-body localized state and its implications for topological order
• Holographic duality from random tensor networks
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Violation of the entropic area law for Fermions
• Entanglement versus Correlations in Spin Systems
• Corner Transfer Matrix Renormalization Group Method
• From density-matrix renormalization group to matrix product states
• Models for gapped boundaries and domain walls
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Entropy scaling and simulability by Matrix Product States
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
• Entanglement spectrum in one-dimensional systems
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Coarse-graining renormalization by higher-order singular value decomposition
• Entropy, entanglement, and area: analytical results for harmonic lattice systems
• TFT construction of RCFT correlators I: Partition functions
• Renormalization and tensor product states in spin chains and lattices
• Topological quantum order: stability under local perturbations
• Matrix product operator representations
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Tensor Network Renormalization
• Sequential generation of entangled multi-qubit states
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• New Trends in Density Matrix Renormalization
• Detection of Symmetry Protected Topological Phases in 1D
• Valence Bond Solids for Quantum Computation
• Scaling of entanglement support for Matrix Product States
• The computational complexity of PEPS
• Towards Quantum Machine Learning with Tensor Networks
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Entanglement spectrum and boundary theories with projected entangled-pair states
• PEPS as ground states: degeneracy and topology
• Dividing Quantum Channels
• Tensor network decompositions in the presence of a global symmetry
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Continuous Matrix Product States for Quantum Fields
• Non-abelian symmetries in tensor networks: a quantum symmetry space approach
• Tensor network states and geometry
• String order and symmetries in quantum spin lattices
• Second Renormalization of Tensor-Network States
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Entanglement renormalization for quantum fields
• Protected edge modes without symmetry
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• Fermionic Projected Entangled Pair States
• Solving Gapped Hamiltonians Locally
• Is Entanglement Monogamous?
• Variational optimization with infinite projected entangled-pair states
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Topological Defects on the Lattice I: The Ising model
• N-representability is QMA-complete
• Gradient methods for variational optimization of projected entangled-pair states
• Renormalization group transformations on quantum states
• Renormalization of tensor-network states
• A short proof of stability of topological order under local perturbations
• Stability of Frustration-Free Hamiltonians
• Entanglement renormalization and topological order
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• Matrix product states for gauge field theories
• Loop optimization for tensor network renormalization
• Entanglement renormalization, scale invariance, and quantum criticality
• Entanglement renormalization in two spatial dimensions
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Anyons and matrix product operator algebras
• Resonating valence bond states in the PEPS formalism
• Index theory of one dimensional quantum walks and cellular automata
• Edge state inner products and real-space entanglement spectrum of trial quantum Hall states
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
• Variational matrix product ansatz for dispersion relations
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Finite automata for caching in matrix product algorithms
• Explicit tensor network representation for the ground states of string-net models
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• An area law for entanglement from exponential decay of correlations
• Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Exact Matrix Product States for Quantum Hall Wave Functions
• Power law violation of the area law in quantum spin chains
• Mapping Kitaev's quantum double lattice models to Levin and Wen's string-net models
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Quantum phase transition in spin-3/2 systems on the hexagonal lattice - optimum ground state approach
• A quantum version of Wielandt's inequality
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Projected entangled-pair states can describe chiral topological states
• The spectral gap for some spin chains with discrete symmetry breaking
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Algorithms for tensor network renormalization
• Compactly-supported Wannier functions and algebraic $K$-theory
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Quantum MERA Channels
• Elementary excitations in gapped quantum spin systems
• An order parameter for symmetry-protected phases in one dimension
• Self-energy-functional theory
• Exact entanglement renormalization for string-net models
• Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
• Finite correlation length scaling with infinite projected entangled-pair states
• Laughlin spin liquid states on lattices obtained from conformal field theory
• Purifications of multipartite states: limitations and constructive methods
• Variational Approach to Projected Entangled Pair States at Finite Temperature
• Calculus of continuous matrix product states
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Geometry of Matrix Product States: metric, parallel transport and curvature
• Holographic quantum states
• Shadows of Anyons
• Mapping topological to conformal field theories through strange correlators
• Transfer Matrices and Excitations with Matrix Product States
• Matrix Product States for Trial Quantum Hall States
• A canonical form for Projected Entangled Pair States and applications
• Vertical Density Matrix Algorithm: A Higher-Dimensional Numerical Renormalization Scheme based on the Tensor Product State Ansatz
• Renormalization group flows of Hamiltonians using tensor networks
• Conformal Data from Finite Entanglement Scaling
• Matrix product operators for symmetry-protected topological phases: Gauging and edge theories
• Half the entanglement in critical systems is distillable from a single specimen
• Broken quantum symmetry and confinement phases in planar physics
• Rigorous RG algorithms and area laws for low energy eigenstates in 1D
• Twisted Injectivity in PEPS and the Classification of Quantum Phases
• Renormalization algorithm for the calculation of spectra of interacting quantum systems
• Chiral topological spin liquids with projected entangled pair states
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Efficient representation of fully many-body localized systems using tensor networks
• Chiral projected entangled-pair state with topological order
• Entanglement phases as holographic duals of anyon condensates
• The computational difficulty of finding MPS ground states
• Quantum phase transition from bounded to extensive entanglement entropy in a frustration-free spin chain
• A scaling hypothesis for matrix product states
• Applying the variational principle to (1+1)-dimensional quantum field theories
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Critical properties of homogeneous binary trees
• Anyon condensation and a generic tensor-network construction for symmetry protected topological phases
• Area law of non-critical ground states in 1D long-range interacting systems
• Fermion condensation and super pivotal categories
• Contracting projected entangled pair states is average-case hard
• Local gap threshold for frustration-free spin systems
• Lattice Model for Fermionic Toric Code
• Characterizing Topological Order with Matrix Product Operators
• Tensor product representation of topological ordered phase: necessary symmetry conditions
• Fermionic projected entangled-pair states and topological phases
• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states
• Particles, holes and solitons: a matrix product state approach
• Edge theories in Projected Entangled Pair State models
• Symmetries and boundary theories for chiral Projected Entangled Pair States
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Extraction of conformal data in critical quantum spin chains using the Koo-Saleur formula
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• A tensor network quotient takes the vacuum to the thermal state
• Matrix Product Representation of Locality Preserving Unitaries
• Spectral gaps of frustration-free spin systems with boundary
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
• Frustration free gapless Hamiltonians for Matrix Product States
• A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• A generalization of the injectivity condition for Projected Entangled Pair States
• Fundamental limitations in the purifications of tensor networks
• Local scale transformations on the lattice with tensor network renormalization
• On the stability of topological phases on a lattice
• Continuous Tensor Network States for Quantum Fields
• Toy Models of Holographic Duality between local Hamiltonians
• Entanglement Renormalization for Weakly Interacting Fields
• Efficient description of many-body systems with Matrix Product Density Operators
• Holographic coherent states from random tensor networks
• Robustness in Projected Entangled Pair States
• Anomalies and entanglement renormalization
• Continuum tensor network field states, path integral representations and the encoding of spatial symmetries
• Normal projected entangled pair states generating the same state
• Microscopic description of 2d topological phases, duality and 3d state sums
• Quantum spin chains with quantum group symmetry
• Real-space renormalization yields finite correlations
• Irreducible forms of Matrix Product States: Theory and Applications
• Area law for fixed points of rapidly mixing dissipative quantum systems
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Gapless Hamiltonians for the toric code using the PEPS formalism
• Projected Entangled Pair States: Fundamental analytical and numerical limitations
• Entanglement, fractional magnetization and long-range interactions
• Symmetry Breaking and Convex Set Phase Diagrams for the q-state Potts Model
• Symmetry Breaking and the Geometry of Reduced Density Matrices
• Truncating an exact Matrix Product State for the XY model: transfer matrix and its renormalisation
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I
• Non-Gaussian Entanglement Renormalization for Quantum Fields
• Product Vacua and Boundary State Models in d Dimensions
• Product vacua with boundary states
• Quantum Gross-Pitaevskii Equation
• The ground state of a class of noncritical 1D quantum spin systems can be approximated efficiently
• Interplay of $SU(2)$, point group and translation symmetry for PEPS: application to a chiral spin liquid
• Global anomaly detection in two-dimensional symmetry-protected topological phases
• Divide and conquer method for proving gaps of frustration free Hamiltonians
• Boson condensation and instability in the tensor network representation of string-net states
• Long range order and symmetry breaking in Projected Entangled Pair State models
• Product vacua with boundary states and the classification of gapped phases
• Entanglement Renormalization for Interacting Field Theories
• Ground state uniqueness of the twelve site RVB spin-liquid parent Hamiltonian on the kagome lattice
• Symmetry reduction induced by anyon condensation: a tensor network approach
• Locality at the boundary implies gap in the bulk for 2D PEPS
• A remark on matrix product operator algebras, anyons and subfactors
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization II
• A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III
• Connected components of irreducible maps and 1D quantum phases
• Integrability and braided tensor categories
• Continuum limits of Matrix Product States
• Perturbation Theory for Parent Hamiltonians of Matrix Product States
• Local order parameters for symmetry fractionalization
• Entanglement compression in scale space: from the multiscale entanglement renormalization ansatz to matrix product operators
• ${\mathbb{Z}}_N$ symmetry breaking in Projected Entangled Pair State models

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• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Contrasting pseudo-criticality in the classical two-dimensional Heisenberg and ${\mathrm{RP}}^2$ models: zero-temperature phase transition versus finite-temperature crossover
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Tensor network decompositions for absolutely maximally entangled states
• Optimal Symbolic Construction of Matrix Product Operators and Tree Tensor Network Operators
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Tensor Network Computations That Capture Strict Variationality, Volume Law Behavior, and the Efficient Representation of Neural Network States
• Optimizing one-axis twists for variational Bayesian quantum metrology
• Bose-Einstein condensation in honeycomb dimer magnets and $\mathrm{Y}{\mathrm{b}}_2\mathrm{S}{\mathrm{i}}_2{\mathrm{O}}_7$
• Charting the space of ground states with tensor networks
• Signatures of quantum criticality in the complex inverse temperature plane
• Dissipative Symmetry-Protected Topological Order
• Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
• Interaction driven topological phase transitions of hardcore bosons on a two-leg ladder
• Extending Non-Perturbative Simulation Techniques for Open-Quantum Systems to Excited-State Proton Transfer and Ultrafast Non-Adiabatic Dynamics
• Symmetric quantum states: a review of recent progress
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Undecidability in Physics: a Review
• Chebyshev pseudosite matrix product state approach for the spectral functions of electron-phonon coupling systems
• Fermionic Isometric Tensor Network States in Two Dimensions
• Pseudo-fermion functional renormalization group with magnetic fields
• The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
• Capturing long-range memory structures with tree-geometry process tensors
• Detecting emergent continuous symmetries at quantum criticality
• Pivoting through the chiral-clock family
• Classical spin Hamiltonians are context-sensitive languages
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• On the Magnetization of the $120^{\circ }$ order of the Spin-1/2 Triangular Lattice Heisenberg Model: a DMRG revisit
• Finite-depth scaling of infinite quantum circuits for quantum critical points
• Privacy-preserving machine learning with tensor networks
• Generalized Gibbs Ensemble Description of Real Space Entanglement Spectra of (2+1)-dimensional Chiral Topological Systems with $SU(2)$ Symmetry
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Locality optimization for parent Hamiltonians of Tensor Networks
• Impact and Interplay of Quantum Coherence and Dissipative Dynamics for Isotope Effects in Excited-State Intramolecular Proton Transfer
• Multinode quantum spin liquids in extended Kitaev honeycomb models: the view from variational Monte Carlo
• Probing the limits of variational quantum algorithms for nonlinear ground states on real quantum hardware: The effects of noise
• Loop Series Expansions for Tensor Networks
• Chiral spin liquids with projected Gaussian fermionic entangled pair states
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Quantum phases of constrained bosons on a two-leg Bose-Hubbard ladder
• Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks
• Topological dualities via tensor networks
• Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics
• Designs from magic-augmented Clifford circuits
• Projected Entangled Pair States with flexible geometry
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Competing States in the Two-Dimensional Frustrated Kondo-Necklace Model
• Entropic relations for indistinguishable quantum particles
• Hopf algebras and solvable unitary circuits
• Dual-isometric Projected Entangled Pair States
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Universal Behavior in Entanglement Entropy Reveals Quantum Criticality and Underlying Symmetry Breaking
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Matrix-product unitaries: Beyond quantum cellular automata
• The Haldane gap in the SU(3) [3 0 0] Heisenberg chain
• Tangent space generators of matrix product states and exact Floquet quantum scars
• Fermionic tensor network contraction for arbitrary geometries
• Exact correlations in topological quantum chains
• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• The resource theory of tensor networks
• Exact Quantum Algorithms for Quantum Phase Recognition: Renormalization Group and Error Correction
• Variational Tensor Network Operator
• Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Probabilistic Inference in the Era of Tensor Networks and Differential Programming
• Single-layer tensor network approach for three-dimensional quantum systems
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Generation of photonic tensor network states with Circuit QED
• Prethermalization by Random Multipolar Driving on a 78-Qubit Superconducting Processor
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Relaxations and Exact Solutions to Quantum Max Cut via the Algebraic Structure of Swap Operators
• Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model
• Energy-filtered quantum states and the emergence of non-local correlations
• Unveiling clean two-dimensional discrete time crystals on a digital quantum computer
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids
• Gauging quantum states with non-anomalous matrix product operator symmetries
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Efficient conversion from fermionic Gaussian states to matrix product states
• Local Jordan-Wigner transformations on the torus
• Preparing matrix product states via fusion: constraints and extensions
• Two-dimensional correlation propagation dynamics with a cluster discrete phase-space method
• Structural Stability Hypothesis of Dual Unitary Quantum Chaos
• Entanglement in dual unitary quantum circuits with impurities
• Universal contributions to charge fluctuations in spin chains at finite temperature
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• From Complexification to Self-Similarity: New Aspects of Quantum Criticality
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
• Detecting Many-Body Scars from Fisher Zeros
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Large-scale stochastic simulation of open quantum systems
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• Tensor networks and efficient descriptions of classical data
• Reviving product states in the disordered Heisenberg chain
• Continuous Wigner-Mott transition at $\nu =1/5$
• A generic quantum Wielandt's inequality
• Finite-Entanglement Scaling of 2D Metals
• Multiparticle singlet states cannot be maximally entangled for the bipartitions
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Embedding semiclassical periodic orbits into chaotic many-body Hamiltonians
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Duality and hidden symmetry breaking in the q-deformed Affleck-Kennedy-Lieb-Tasaki model
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Dual-VQE: A quantum algorithm to lower bound the ground-state energy
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward
• Internal structure of gauge-invariant Projected Entangled Pair States
• Quantum Gauge Networks: A New Kind of Tensor Network
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Fractional domain wall statistics in spin chains with anomalous symmetries
• Multi-orbital two-particle self-consistent approach -- strengths and limitations
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Many-body computing on Field Programmable Gate Arrays
• Spectral Gap Optimization for Enhanced Adiabatic State Preparation
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Reconstruction of Quantum Particle Statistics: Bosons, Fermions, and Transtatistics
• The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition
• TensorKrowch: Smooth integration of tensor networks in machine learning
• Parent Hamiltonian as a benchmark problem for variational quantum eigensolvers
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Conditional global entanglement in a Kosterlitz-Thouless quantum phase transition
• Entanglement at the interplay between single- and many-bodyness
• Wilson loops in the Hamiltonian formalism
• Optimization via Quantum Preconditioning
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Accelerating two-dimensional tensor network optimization by preconditioning
• Simulating Quantum Turbulence with Matrix Product States
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Searching for superconductivity in doped triangular lattice Kitaev magnets
• Quantum generative modeling for financial time series with temporal correlations
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Tangent Space Excitation Ansatz for Quantum Circuits
• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Scalable projected entangled-pair state representation of random quantum circuit states
• Multipartite Entanglement Structure of Fibered Link States
• The surface code beyond Pauli channels: Logical noise coherence, information-theoretic measures, and errorfield-double phenomenology
• Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers
• Non-Landau quantum phase transition in modulated SU(N) Heisenberg spin chains
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Cost of Locally Approximating High-Dimensional Ground States of Contextual Quantum Models
• Dual-unitary shadow tomography
• PAC-learning of free-fermionic states is NP-hard
• Nonlocal order parameter of pair superfluids
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• The Cytnx Library for Tensor Networks
• Efficient Learning of Long-Range and Equivariant Quantum Systems
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• Adaptive measurement strategy for quantum subspace methods
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Solving Fermi-Hubbard-type Models by Tensor Representations of Backflow Corrections
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Identifying families of multipartite states with non-trivial local entanglement transformations
• A quantum inspired approach to learning dynamical laws from data -- block-sparsity and gauge-mediated weight sharing
• Quantized and maximum entanglement from sublattice symmetry
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Variational optimization of projected entangled-pair states on the triangular lattice
• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• Chain-mapping methods for relativistic light-matter interactions
• Symmetries and field tensor network states
• Classifying fermionic states via many-body correlation measures
• A Hermitian bypass to the non-Hermitian quantum theory
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• The Tensor as an Informational Resource
• CTMRG study of the critical behavior of an interacting-dimer model
• Parent Hamiltonian for Fully-augmented Matrix Product States
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Quantum Magnetic Skyrmions on Kondo-type Lattices
• Effects of Topological Boundary Conditions on Bell Nonlocality
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Universal quasi-Fermi liquid physics of one-dimensional interacting fermions
• Efficient inference of quantum system parameters by Approximate Bayesian Computation
• Entanglement spectra of non-chiral topological (2+1)-dimensional phases with strong time-reversal breaking, Li-Haldane state counting, and PEPS
• Entanglement dynamics from universal low-lying modes
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Critical Fermions are Universal Embezzlers
• Non-Universality from Conserved Superoperators in Unitary Circuits
• Threefold Way for Typical Entanglement
• Pseudoentanglement from tensor networks
• Post-measurement Quantum Monte Carlo
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
• A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems
• Robustness of near-thermal dynamics on digital quantum computers
• Competing pair density wave orders in the square lattice $t$-$J$ model
• Gaussian matrix product states cannot efficiently describe critical systems
• Boundary-induced singularity in strongly-correlated quantum systems at finite temperature
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Magnetic phases of the periodic Anderson model in two dimensions
• Parent Lindbladians for Matrix Product Density Operators
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Frustration-free free fermions
• Frustration-free free fermions and beyond
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• Quantum Many-Body Linear Algebra, Hamiltonian Moments, and a Coupled Cluster Inspired Framework
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach
• Gauging Quantum Phases: A Matrix Product State Approach
• ScarFinder: a detector of optimal scar trajectories in quantum many-body dynamics
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers
• The ITransverse.jl library for transverse tensor network contractions
• Border Ranks of Positive and Invariant Tensor Decompositions: Applications to Correlations
• Bound on entanglement in neural quantum states
• Reconfigurable dissipative entanglement between many spin ensembles: from robust quantum sensing to many-body state engineering
• Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
• Les Houches Lecture Notes on Tensor Networks
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Partial Degeneration of Tensors
• Efficiency of neural-network state representations of one-dimensional quantum spin systems
• Towards Symmetry-Aware Efficient Simulation of Quantum Systems and Beyond
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators
• Equivalence of residual entropy of hexagonal and cubic ices from tensor network methods
• Finding periodic orbits in projected quantum many-body dynamics
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Partons from stabilizer codes
• The abelian state hidden subgroup problem: Learning stabilizer groups and beyond
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Probing universal imaginary-time relaxation critical dynamics with infinite projected entangled pair states
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Universal entanglement correction induced by relevant deformations at the quantum critical point
• General many-body entanglement swapping protocol: opportunities for distributed quantum computing
• Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra
• Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method
• Energy Spectra of Compressed Quantum States
• Emergence of topological defects and spin liquid in a two-orbital spin-fermion model on the honeycomb lattice
• Quantum Machine Learning for State Tomography Using Classical Data
• Learning mixed quantum states in large-scale experiments
• Skeleton of isometric Tensor Network States for Abelian String-Net Models
• Quantum Circuits for Matrix-Product Unitaries
• Capturing reduced-order quantum many-body dynamics out of equilibrium via neural ordinary differential equations
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
• Efficient tomography of microwave photonic cluster states
• The product structure of MPS-under-permutations
• Holographic Tensor Networks as Tessellations of Geometry
• Non-local order parameters for fermion chains via the partial transpose
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Exact large deviations and emergent long-range correlations in sequential quantum East circuits
• Anderson localization: a density matrix approach
• Entanglement as a topological marker in harmonically confined attractive Fermi-Hubbard chains
• A minimal tensor network beyond free fermions
• Vanishing correlations in stochastic and bistochastic controlled circuits
• Symmetry-enforced minimal entanglement and correlation in quantum spin chains
• Using matrix-product states for time-series machine learning
• Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• Grassmann tensor networks
• Tensorization of neural networks for improved privacy and interpretability
• Adaptive time Compressed QITE (ACQ) and its geometrical interpretation
• Quantitative Description of Strongly Correlated Materials by Combining Downfolding Techniques and Tensor Networks
• The Canonical Forms of Matrix Product States in Infinite-Dimensional Hilbert Spaces
• Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
• Dynamical cluster-based strategy for improving tensor network algorithms in quantum circuit simulations
• Chiral Edge Excitations of $\nu =1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model
• Emulation of large-scale qubit registers with a phase-space approach
• Exact Fractionalized Ground States in an Extended Spin-1 Kitaev Chain
• Continuous matrix product operators for quantum fields
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition