A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States

Abstract

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed.

51 pages, 45 figures, minor typos corrected. Accepted for publication in Annals of Physics

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• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Deep Learning of Quantum Many-Body Dynamics via Random Driving
• A Pairwise Connected Tensor Network Representation of Path Integrals
• Detecting and identifying 2D symmetry-protected topological, symmetry-breaking and intrinsic topological phases with modular matrices via tensor-network methods
• Quantum gravity states, entanglement graphs and second-quantized tensor networks
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Optimal sampling of dynamical large deviations in two dimensions via tensor networks
• Matrix product states and the nonabelian rotor model
• Spacetime as a quantum circuit
• Phase Diagram of the Spin-$1/2$ Triangular $J_1$-$J_2$ Heisenberg Model on a 3-leg Cylinder
• Benchmarking Quantum Computer Simulation Software Packages: State Vector Simulators
• Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr${}_2$RuO${}_4$
• The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases
• Magnetization of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice
• Fisher Metric, Geometric Entanglement and Spin Networks
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Long-Range Entangled-Plaquette States for Critical and Frustrated Quantum Systems on a Lattice
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Optimal stochastic unraveling of disordered open quantum systems: application to driven-dissipative photonic lattices
• Preparing quantum many-body scar states on quantum computers
• Enhanced TEMPO algorithm for quantum path integrals with off-diagonal system-bath coupling: applications to photonic quantum networks
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations
• Emergent behaviors in group ring flocks
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
• Modeling Sequences with Quantum States: A Look Under the Hood
• Emerging dynamics arising from coarse-grained quantum systems
• Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice
• Properties of exotic nuclei and their linkage to the nucleonic interaction
• Hilbert space delocalization under random unitary circuits
• Dynamical quantum phase transitions of the Schwinger model: real-time dynamics on IBM Quantum
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics
• Calibrating the role of entanglement in variational quantum circuits
• Critical light-matter entanglement at cavity mediated phase transition
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices
• The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Density-matrix renormalization group: a pedagogical introduction
• Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
• Quantum Machine Learning Tensor Network States
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• A tree tensor network approach to simulating Shor's algorithm
• Growth of genuine multipartite entanglement in random unitary circuits
• Analysis of quantum spin models on hyperbolic lattices and Bethe lattice
• Supersolid-Superfluid phase separation in the extended Bose-Hubbard model
• Finite-Temperature Variational Monte Carlo Method for Strongly Correlated Electron Systems
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Approximate optimization, sampling and spin-glass droplets discovery with tensor networks
• Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings
• Free-fermion descriptions of parafermion chains and string-net models
• Computing partial traces and reduced density matrices
• Systematic construction of density functionals based on matrix product state computations
• Mutual Information Scaling for Tensor Network Machine Learning
• Variational Renormalization Group for Dissipative Spin-Cavity Systems: Periodic Pulses of Nonclassical Photons from Mesoscopic Spin Ensembles
• Dealing with the exponential wall in electronic structure calculations
• Interaction driven polarization shift in the $t-V-V^{\prime }$ lattice fermion model at half filling: emergent Haldane phase
• Stabilizer disentangling of conformal field theories
• Exact stabilization of entangled states in finite time by dissipative quantum circuits
• Tensor networks for quantum computing
• Recent progress on quantum simulations of non-standard Bose-Hubbard models
• Continuous phase transition between Neel and valence bond solid phases in a J-Q-like spin ladder system
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Approximating local observables on projected entangled pair states
• Exploring the CP-violating Dashen phase in the Schwinger model with tensor networks
• Quantum Compressed Sensing with Unsupervised Tensor-Network Machine Learning
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Qubitization strategies for bosonic field theories
• Approximate encoding of quantum states using shallow circuits
• Entanglement estimation in tensor network states via sampling
• Computing exact moments of local random quantum circuits via tensor networks
• Locating quantum critical points with Kibble-Zurek quenches
• Renormalising entanglement distillation
• Classical algorithms for many-body quantum systems at finite energies
• Exact holographic tensor networks for the Motzkin spin chain
• Opening the Black Box Inside Grover's Algorithm
• Language Design as Information Renormalization
• Energy cost of entanglement extraction in complex quantum systems
• Disorder-free localization in quantum walks
• Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes
• The Heisenberg limit for laser coherence
• Simulating topological tensor networks with Majorana qubits
• Topological spin phases of trapped Rydberg excitons in Cu${}_2$O
• Quantum Quench and Charge Oscillations in the SU(3) Hubbard Model: a Test of Time Evolving Block Decimation with general non-Abelian Symmetries
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Electronic Correlation and Geometrical Frustration in Molecular Solids -- A Systematic ab initio Study of ${\beta }^{\prime }$-$X$[Pd(dmit)${}_2$]${}_2$
• Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions
• Reduced-Rank Tensor-on-Tensor Regression and Tensor-variate Analysis of Variance
• Density-operator evolution: Complete positivity and the Keldysh real-time expansion
• Doped stabilizer states in many-body physics and where to find them
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Beyond mean-field dynamics of ultra-cold bosonic atoms in higher dimensions: facing the challenges with a multi-configurational approach
• Neural Network Operations and Susuki-Trotter evolution of Neural Network States
• Extracting Quantum Many-Body Scarred Eigenstates with Matrix Product States
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
• Phase Transitions for quantum Ising model with competing XY -interactions on a Cayley tree
• QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
• Tensor network simulation of the quantum Kibble-Zurek quench from the Mott to superfluid phase in the two-dimensional Bose-Hubbard model
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• Long range order and symmetry breaking in Projected Entangled Pair State models
• From observations to complexity of quantum states via unsupervised learning
• Quantum simulations of a qubit of space
• Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• TeNeS: Tensor Network Solver for Quantum Lattice Systems
• Efficient representation of long-range interactions in tensor network algorithms
• Tensor Network Decoding Beyond 2D
• jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
• Tangent-Space Gradient Optimization of Tensor Network for Machine Learning
• Scaling Whole-Chip QAOA for Higher-Order Ising Spin Glass Models on Heavy-Hex Graphs
• First-Order Phase Transition of the Schwinger Model with a Quantum Computer
• Surrogate models for quantum spin systems based on reduced order modeling
• Quantum algorithms for scientific computing
• Quantum-classical eigensolver using multiscale entanglement renormalization
• Gaussian Process States: A data-driven representation of quantum many-body physics
• Planar Maximally Entangled States
• Renormalization Group Circuits for Gapless States
• Fermionic algebraic quantum spin liquid in an octa-kagome frustrated antiferromagnet
• Efficient evaluation of high-order moments and cumulants in tensor network states
• Holographic maps from quantum gravity states as tensor networks
• Ryu-Takayanagi Formula for Symmetric Random Tensor Networks
• Search for localized Wannier functions of topological band structures via compressed sensing
• Block belief propagation algorithm for two-dimensional tensor networks
• Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation
• Qibolab: an open-source hybrid quantum operating system
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• Efficient Quantum Simulation for Thermodynamics of Infinite-size Many-body Systems in Arbitrary Dimensions
• From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics
• Fast trimers in one-dimensional extended Fermi-Hubbard model
• Stabilizer Tensor Networks with Magic State Injection
• Optimization at the boundary of the tensor network variety
• The Bethe Ansatz as a Quantum Circuit
• Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities
• Phase structure of the 1+1 dimensional massive Thirring model from matrix product states
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• Q${}^2$Chemistry: A quantum computation platform for quantum chemistry
• Tensor network representations from the geometry of entangled states
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Time evolution of coupled spin systems in a generalized Wigner representation
• Symmetries and entanglement of stabilizer states
• Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization
• Relating the curvature of De Sitter Universe to Open Quantum Lamb Shift Spectroscopy
• Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization
• Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
• Quantum droplets with particle imbalance in one-dimensional optical lattices
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Combined tensor network/cluster expansion method using logic gates: Illustrated for (bi-)excitons by a single layer MoS${}_2$ model system
• Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
• Density of Yang-Lee zeros in the thermodynamic limit from tensor network methods
• Ground state search by local and sequential updates of neural network quantum states
• Unifying view of fermionic neural network quantum states: From neural network backflow to hidden fermion determinant states
• Phase diagram of Rydberg-dressed atoms on two-leg triangular ladders
• Locality at the boundary implies gap in the bulk for 2D PEPS
• Noise effects on purity and quantum entanglement in terms of physical implementability
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Renormalization of group field theories for quantum gravity: new scaling results and some suggestions
• Calibrating the Classical Hardness of the Quantum Approximate Optimization Algorithm
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• A relativistic discrete spacetime formulation of 3+1 QED
• Entanglement spectrum of mixed states
• All spin-1 topological phases in a single spin-2 chain
• Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Spin-one bilinear-biquadratic model on a star lattice
• Variational determination of multi-qubit geometrical entanglement in NISQ computers
• Optimization schemes for unitary tensor-network circuit
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Neural Projected Quantum Dynamics: a systematic study
• Anticoncentration and state design of random tensor networks
• Multipartite correlations in quantum collision models
• Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval
• Stable bipolarons in open quantum systems
• On the closedness and geometry of tensor network state sets
• Approximating the long time average of the density operator: Diagonal ensemble
• Conformal Properties of Hyperinvariant Tensor Networks
• Matrix product state representation of quasielectron wave functions
• Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
• Topological quantum synchronization of fractionalized spins
• Link representation of the entanglement entropies for all bipartitions
• Mott Quantum Criticality in the Anisotropic 2D Hubbard Model
• From spin chains to real-time thermal field theory using tensor networks
• Quantum phases of dipolar bosons in one-dimensional optical lattices
• Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions
• Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
• Theory of intervalley-coherent AFM order and topological superconductivity in tWSe${}_2$
• Tensor renormalization group in bosonic field theory
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Geometric entanglement and quantum phase transitions in two-dimensional quantum lattice models
• Boundary theories of critical matchgate tensor networks
• Classification of symmetry-protected topological phases in two-dimensional many body-localized systems
• Hybrid Berezinskii-Kosterlitz-Thouless and Ising topological phase transition in the generalized two-dimensional XY model using tensor networks
• Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States
• Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain
• Entanglement Hamiltonians and the quasiparticle picture
• Tensor network noise characterization for near-term quantum computers
• Data-driven compression of electron-phonon interactions
• Certifying ground-state properties of quantum many-body systems
• Uhlmann fidelities from tensor networks
• Converting long-range entanglement into mixture: tensor-network approach to local equilibration
• QFactor: A Domain-Specific Optimizer for Quantum Circuit Instantiation
• Probing critical states of matter on a digital quantum computer
• Quantifying Rare Events in Stochastic Reaction-Diffusion Dynamics Using Tensor Networks
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Entanglement in the quantum phases of an unfrustrated Rydberg atom array
• Translating Uncontrolled Systems in Time
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• From Tree Tensor Network to Multiscale Entanglement Renormalization Ansatz
• Operatorial formulation of the ghost rotationally-invariant slave-Boson theory
• Efficient simulation of ultrafast quantum nonlinear optics with matrix product states
• Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
• Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems
• Global optimization of tensor renormalization group using the corner transfer matrix
• Benchmarking global $SU(2)$ symmetry in 2d tensor network algorithms
• Wilson line networks in $p$-adic AdS/CFT
• Integrability breaking in the Rule 54 cellular automaton
• User-friendly TWA for dissipative spin dynamics
• Sample-efficient estimation of entanglement entropy through supervised learning
• Graph-associated entanglement cost of a multipartite state in exact and finite-block-length approximate constructions
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice
• A framework for efficient ab initio electronic structure with Gaussian Process States
• Bond order via cavity-mediated interactions
• Partitioning Quantum Chemistry Simulations with Clifford Circuits
• Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?
• Entanglement and confinement in lattice gauge theory tensor networks
• Fine-Grained Tensor Network Methods
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• Magic phase transition and non-local complexity in generalized $W$ State
• Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems
• Collective Monte Carlo updates through tensor network renormalization
• Classification of symmetry-protected topological many-body localized phases in one dimension
• Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states
• Disentangling critical quantum spin chains with Clifford circuits
• Polynomial scaling enhancement in ground-state preparation of Ising spin models via counter-diabatic driving
• Symmetry protected phases in inhomogeneous spin chains
• Improving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learning
• Undecidability of the Spectral Gap (full version)
• On the generalization of the exponential basis for tensor network representations of long-range interactions in two and three dimensions
• Structured quantum collision models: generating coherence with thermal resources
• Variational quantum state preparation via quantum data buses
• Time-dependent spectral properties of photoexcited one-dimensional ionic Hubbard model: an exact diagonalization study
• Functional Tensor Network Solving Many-body Schrödinger Equation
• Quantum state preparation for multivariate functions
• Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• On the descriptive power of Neural-Networks as constrained Tensor Networks with exponentially large bond dimension
• Tensor network strategies for calculating biexcitons and trions in monolayer 2D materials beyond the ground state
• Adaptive variational low-rank dynamics for open quantum systems
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Machine learning with tree tensor networks, CP rank constraints, and tensor dropout
• Fermionic wave packet scattering: a quantum computing approach
• Avalanche terahertz photon detection in a Rydberg tweezer array
• Doublon dynamics of Bose-Fermi mixtures in optical lattices
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• Dimension of Tensor Network varieties
• A Bayesian Inference Framework for Compression and Prediction of Quantum States
• Multi-Region Entanglement in Locally Scrambled Quantum Dynamics
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Topological phases of an interacting Majorana Benalcazar-Bernevig-Hughes model
• 2D Quantum Double Models From a 3D Perspective
• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Simulation of braiding anyons using Matrix Product States
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• Entanglement Area Law for Shallow and Deep Quantum Neural Network States
• Stabilizer Rényi Entropy and Conformal Field Theory
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
• Boundary conditions dependence of the phase transition in the quantum Newman-Moore model
• A graphical calculus for integration over random diagonal unitary matrices
• Continuum limits of Matrix Product States
• Quantum many-body simulations with PauliStrings.jl
• Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• Quantum Many-Body Scarring in a Non-Abelian Lattice Gauge Theory
• The seniority quantum number in Tensor Network States
• Holographic entanglement in spin network states: a focused review
• Experimental Simulation of Loop Quantum Gravity on a Photonic Chip
• Lanczos steps to improve variational wave functions
• Probing infinite many-body quantum systems with finite-size quantum simulators
• Faster variational quantum algorithms with quantum kernel-based surrogate models
• Circuit Complexity through phase transitions: consequences in quantum state preparation
• Reduced basis surrogates for quantum spin systems based on tensor networks
• Certificates of quantum many-body properties assisted by machine learning
• NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization
• Compact Neural-network Quantum State representations of Jastrow and Stabilizer states
• Half a state, half an operator: a general formulation of stators
• Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States
• Quantum tomography of magnons using Brillouin light scattering
• Matrix product state fixed points of non-Hermitian transfer matrices
• Process tensor approaches to modeling two-dimensional spectroscopy
• Hybrid Tree Tensor Networks for quantum simulation
• Measurement outcomes that do not occur and their role in entanglement transformations
• Inhomogeneity induced shortcut to adiabaticity in Ising chains with long-range interactions
• Matrix product states and the quantum max-flow/min-cut conjectures
• Tensor network Monte Carlo simulations for the two-dimensional random-bond Ising model
• Quantum criticality in the 2d quasiperiodic Potts model
• Automatic Contraction of Unstructured Tensor Networks
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Interplay of entanglement structures and stabilizer entropy in spin models
• Thermal bosons in 3d optical lattices via tensor networks
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Quantum correlated cluster mean-field theory applied to the transverse Ising model
• How local is the information in MPS/PEPS tensor networks?
• Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method
• A continuum of compass spin models on the honeycomb lattice
• Continuous matrix product states solution for the mixing/demixing transition in one-dimensional quantum fields
• Approximation of Quantum States Using Decision Diagrams
• Cavitylike strong coupling in macroscopic waveguide QED using three coupled qubits in the deep non-Markovian regime
• A variational method for integrability-breaking Richardson-Gaudin models
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks
• Comparative study of the density matrix embedding theory for the Hubbard models
• Sine-square deformed mean-field theory
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Efficient neural-network based variational Monte Carlo scheme for direct optimization of excited energy states in frustrated quantum systems
• Quantum criticality on a chiral ladder: an $SU(2)$ iDMRG study
• Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices
• Area Law Violations and Quantum Phase Transitions in Modified Motzkin Walk Spin Chains
• Rényi free energy and variational approximations to thermal states
• 2500 vibronic eigenstates of the NO${}_3$ radical
• Refinement of quantum Markov states on trees
• Time dependent Markovian master equation beyond the adiabatic limit
• Coherent spin-phonon scattering in facilitated Rydberg lattices
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Locally purified density operators for noisy quantum circuits
• Partonic distribution functions and amplitudes using tensor network methods
• Local Transformations of Multiple Multipartite States
• A simplified and improved approach to tensor network operators in two dimensions
• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Thermal cycle and polaron formation in structured bosonic environments
• Amorphous quantum magnets in a two-dimensional Rydberg atom array
• Scalar mesons in the chiral theory with quark degrees of freedom
• Holographic Quenches with a Gap
• Pair density wave, unconventional superconductivity, and non-Fermi liquid quantum critical phase in frustrated Kondo lattice
• Comparison of the Iterated Equation of Motion Approach and the Density Matrix Formalism for the Quantum Rabi Model
• Density of States of the lattice Schwinger model
• Tensor product variational formulation applied to pentagonal lattice
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• Efficient calculation of three-dimensional tensor networks
• Generation of Bose-Einstein Condensates' Ground State Through Machine Learning
• Two-dimensional algebra in lattice gauge theory
• Tensor Networks for Explainable Machine Learning in Cybersecurity
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Quantum phase transition between spin liquid and spin nematics in spin-1 Kitaev honeycomb model
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Adversarial Robustness Guarantees for Quantum Classifiers
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Entropy scaling law and the quantum marginal problem
• Topological Minimally Entangled States via Geometric Measure
• Local order parameters for symmetry fractionalization
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• Tensor Renormalization Group Centered About a Core Tensor
• The power and limitations of learning quantum dynamics incoherently
• Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations
• Enhancing the efficiency of quantum annealing via reinforcement: A path-integral Monte Carlo simulation of the quantum reinforcement algorithm
• Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
• Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
• Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
• Efficient Decomposition of High-Rank Tensors
• Applications and resource reductions in measurement-based variational quantum eigensolvers
• Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formats
• Many-body molecule formation at a domain wall in a one-dimensional strongly interacting ultracold Fermi gas
• Many-body quantum sign structures as non-glassy Ising models
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Optimizing one-axis twists for variational Bayesian quantum metrology
• Stochastic thermodynamic bounds on logical circuit operation
• Fermionic Magic Resources of Quantum Many-Body Systems
• Signatures of quantum criticality in the complex inverse temperature plane
• Reconstructing Non-Markovian Open Quantum Evolution From Multi-time Measurements
• Measures of distinguishability between stochastic processes
• Connector tensor networks: a renormalization-type approach to quantum certification
• Entanglement and spectra in topological many-body localized phases
• Variational Tensor Neural Networks for Deep Learning
• The antiferromagnetic cross-coupled spin ladder: quantum fidelity and tensor networks approach
• Dissipative Symmetry-Protected Topological Order
• Ab-initio tree-tensor-network digital twin for quantum computer benchmarking in 2D
• Low-rank tensor approximations for solving multi-marginal optimal transport problems
• Meson content of entanglement spectra after integrable and nonintegrable quantum quenches
• Many-body entanglement and topology from uncertainties and measurement-induced modes
• Entanglement and complexity of interacting qubits subject to asymmetric noise
• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method
• Algorithms for Tensor Network Contraction Ordering
• Wilson Loops and Area Laws in Lattice Gauge Theory Tensor Networks
• Continuum approach to real time dynamics of 1+1D gauge field theory: out of horizon correlations of the Schwinger model
• Fast quantum state preparation and bath dynamics using non-Gaussian variational ansatz and quantum optimal control
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Thermal Tensor Network Simulations of the Heisenberg Model on the Bethe Lattice
• Aspects of quantum information in finite density field theory
• Tensor network analysis of the maple-leaf antiferromagnet spangolite
• Floquet Analysis of Frequency Collisions
• On Two Invariants of Three Manifolds from Hopf Algebras
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Separability gap and large deviation entanglement criterion
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Transformer Wave Function for Quantum Long-Range models
• Quantum Markov Chains on the Comb graphs: Ising model
• Stack operation of tensor networks
• Bounding the finite-size error of quantum many-body dynamics simulations
• Topological Spin Liquids: Robustness under perturbations
• Holographic encoding of universality in corner spectra
• Verifying the output of quantum optimizers with ground-state energy lower bounds
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Measuring energy by measuring any other observable
• Tensorized orbitals for computational chemistry
• Entanglement Scaling in Quantum Advantage Benchmarks
• A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems
• Squashed entanglement in one-dimensional quantum matter
• Unraveling long-time quantum dynamics using flow equations
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Exactly solvable subspaces of non-integrable spin chains with boundaries and quasiparticle interactions
• Classification of trivial spin-1 tensor network states on a square lattice
• Measuring out quasi-local integrals of motion from entanglement
• Frustration-free Hamiltonians supporting Majorana zero edge modes
• TNQMetro: Tensor-network based package for efficient quantum metrology computations
• Hilbert space renormalization for the many-electron problem
• Nearly degenerate ground states of a checkerboard antiferromagnet and their bosonic interpretation
• The spatiotemporal doubled density operator: a unified framework for analyzing spatial and temporal quantum processes
• Symmetry-protected intermediate trivial phases in quantum spin chains
• Heralded Optical Entanglement Generation via the Graph Picture of Linear Quantum Networks
• Anderson impurity solver integrating tensor network methods with quantum computing
• Gapless Spin Liquid and Non-local Corner Excitation in the Spin-1/2 Heisenberg Antiferromagnet on Fractal
• Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states
• Extending Non-Perturbative Simulation Techniques for Open-Quantum Systems to Excited-State Proton Transfer and Ultrafast Non-Adiabatic Dynamics
• Expectation values of Coherent States for $\mathrm{SU}(2)$ Lattice Gauge Theories
• Many-body localization regime for cavity induced long-range interacting models
• Entanglement properties of the two-dimensional SU(3) AKLT state
• Combination of Tensor Network States and Green's function Monte Carlo
• Tensor-network approach to thermalization in open quantum many-body systems
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States
• Competing States in the Two-Dimensional Frustrated Kondo-Necklace Model
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Computing quantum magic of state vectors
• Impact and Interplay of Quantum Coherence and Dissipative Dynamics for Isotope Effects in Excited-State Intramolecular Proton Transfer
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Almost Strong Zero Modes at Finite Temperature
• From quantum-enhanced to quantum-inspired Monte Carlo
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Loop Series Expansions for Tensor Networks
• Quantum circuit compilation with quantum computers
• Projected Entangled Pair States with flexible geometry
• Supercell Wannier functions and a faithful low-energy model for Bernal bilayer graphene
• Open quantum dynamics with variational non-Gaussian states and the truncated Wigner approximation
• Quantum Mini-Apps: A Framework for Developing and Benchmarking Quantum-HPC Applications
• Probing the limits of variational quantum algorithms for nonlinear ground states on real quantum hardware: The effects of noise
• Topological dualities via tensor networks
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Adiabatic time evolution of highly excited states
• Emergent information dynamics in many-body interconnected systems
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation
• Growing Schrödinger's cat states by local unitary time evolution of product states
• Optimized Laser Models with Heisenberg-Limited Coherence and Sub-Poissonian Beam Photon Statistics
• Signatures of Non-Markovianity in Cavity-QED with Color Centers in 2D Materials
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• A quantum information perspective on meson melting
• Phase diagram of 1+1D Abelian-Higgs model and its critical point
• Repulsive dynamics of strongly attractive one-dimensional quantum gases
• Language Modeling with Reduced Densities
• Complete aggregation of the Lohe tensor model with the same free flow
• Bosonic entanglement renormalization circuits from wavelet theory
• Simulating fermions in spin-dependent potentials with spin models on an energy lattice
• Méthodes de calcul avec réseaux de tenseurs en physique (Basic tensor network computations in physics)
• Topological phases in two-legged Heisenberg ladders with alternating interactions
• Point-coupling Hamiltonian for frequency-independent linear optical devices
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• Finite entanglement properties in the matrix product states of the one-dimensional Hubbard model
• Single-shot holographic compression from the area law
• Tensor-network approach to compute genuine multisite entanglement in infinite quantum spin chains
• Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model
• Composite symmetry protected topological order and effective models
• Approximate symmetries of Hamiltonians
• Tensor-network algorithm for nonequilibrium relaxation in the thermodynamic limit
• Critical Space-Time Networks and Geometric Phase Transitions from Frustrated Edge Antiferromagnetism
• Cluster-factorized steady states in finite range processes
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices
• Ground-state wavefunction of macroscopic electron systems
• Limitations of tensor network approaches for optimization and sampling: A comparison to quantum and classical Ising machines
• On the Schrödinger-Lohe hierarchy for aggregation and its emergent dynamics
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Liouville Space Neural Network Representation of Density Matrices
• Forestalled Phase Separation as the Precursor to Stripe Order
• Triggering Boundary Phase Transitions through Bulk Measurements in 2D Cluster States
• Entanglement Continuous Unitary Transformations
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Specialising Neural-network Quantum States for the Bose Hubbard Model
• Spectral properties of critical 1+1D Abelian-Higgs model
• Holographic Dynamics from Multiscale Entanglement Renormalization Ansatz
• Picturing Counting Reductions with the ZH-Calculus
• Learning parameter dependence for Fourier-based option pricing with tensor trains
• Differentiable matrix product states for simulating variational quantum computational chemistry
• Quantum phases of spin-1 system on 3/4 and 3/5 skewed ladders
• Segmenting two-dimensional structures with strided tensor networks
• Emergent geometry and path integral optimization for a Lifshitz action
• Non-stabilizerness of Neural Quantum States
• Exploring Disordered Quantum Spin Models with a Multi-Layer Multi-Configurational Approach
• Long-time equilibration can determine transient thermality
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder
• Dynamical scaling laws in the quantum $q$-state clock chain
• Generation of photonic tensor network states with Circuit QED
• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• Low-temperature Gibbs states with tensor networks
• Optimizing Radiotherapy Plans for Cancer Treatment with Tensor Networks
• Entanglement of a alternating bipartition in spin chains: Relation with classical integrable models
• Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers
• Avoidance, Adjacency, and Association in Distributed Systems Design
• Boltzmann machines and quantum many-body problems
• Efficient computations of quantum canonical Gibbs state in phase space
• Fractal states of the Schwinger model
• Approximating Hamiltonian dynamics with the Nyström method
• Exact spectral form factors of non-interacting fermions with Dyson statistics
• Probabilistic Inference in the Era of Tensor Networks and Differential Programming
• Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz
• Entropy of Quantum Markov states on Cayley trees
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Ground state of many-electron systems based on the action function
• Variational Tensor Network Operator
• Meson thermalization with a hot medium in the open Schwinger model
• Efficient conversion from fermionic Gaussian states to matrix product states
• A Matrix Product State Model for Simultaneous Classification and Generation
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• Practical variational tomography for critical 1D systems
• Tensor tree learns hidden relational structures in data to construct generative models
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Quantum Ising model in a period-2 modulated transverse field
• Revisiting the Fermion Sign Problem from the Structure of Lee-Yang Zeros. I. The Form of Partition Function for Indistinguishable Particles and Its Zeros at 0~K
• An efficient perturbation theory of density matrix renormalization group
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• The Role of Quantum Computing in Advancing Scientific High-Performance Computing: A perspective from the ADAC Institute
• A construction of Combinatorial NLTS
• Non-Markovian effects in stochastic resonance in a two level system
• Prethermalization of quantum systems interacting with non-equilibrium environments
• Surveying structural complexity in quantum many-body systems
• Extracting Off-Diagonal Order from Diagonal Basis Measurements
• Computing excited eigenstates using inexact Lanczos methods and tree tensor network states
• Polarized edge state emission from topological spin phases of trapped Rydberg excitons in Cu${}_2$O
• Multiparticle singlet states cannot be maximally entangled for the bipartitions
• Controlling quantum many-body systems using reduced-order modelling
• Approximation in the extended functional tensor train format
• Shaded Tangles for the Design and Verification of Quantum Programs (Extended Abstract)
• Scalable multiphoton generation from cavity-synchronized single-photon sources
• Many-body correlations in one-dimensional optical lattices with alkaline-earth(-like) atoms
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• H-wave -- A Python package for the Hartree-Fock approximation and the random phase approximation
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• Detecting Many-Body Scars from Fisher Zeros
• Uncoupled Majorana fermions in open quantum systems: On the efficient simulation of non-equilibrium stationary states of quadratic Fermi models
• Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
• Making Quantum Collision Models Exact
• Improved real-space parallelizable matrix-product state compression and its application to unitary quantum dynamics simulation
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Disentanglement Approach to Quantum Spin Ground States: Field Theory and Stochastic Simulation
• Quantum Circuit Simulation with Fast Tensor Decision Diagram
• Effective One-Dimensional Models from Matrix Product States
• Quantum correlations of a two-qubit system and the Aubry-André chain in bosonic environments
• Simulating quantum circuits using the multi-scale entanglement renormalization ansatz
• Loop update for infinite projected entangled-pair states in two spatial dimensions
• TensorKrowch: Smooth integration of tensor networks in machine learning
• Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach
• Adiabatic freezing of entanglement with insertion of defects in a one-dimensional Hubbard model
• Tensor Renormalization Group for interacting quantum fields
• Quantum dynamics of cosmological particle production: interacting quantum field theories with matrix product states
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Straddling-gates problem in multipartite quantum systems
• Bell-type correlation at quantum phase transitions in spin-1 chain
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Automatic Structural Search of Tensor Network States including Entanglement Renormalization
• Understanding and utilizing the inner bonds of process tensors
• Sampling Problems on a Quantum Computer
• Non-linear classification capability of quantum neural networks due to emergent quantum metastability
• Measuring multipartite quantum correlations by thermodynamic work extraction
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Quantum-inspired clustering with light
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Deconfined quantum criticality of frustrated hard-core dipolar bosons
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
• Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices
• Survey on Computational Applications of Tensor Network Simulations
• Hyperoptimized approximate contraction of tensor networks for rugged-energy-landscape spin glasses on periodic square and cubic lattices
• Hacking Cryptographic Protocols with Advanced Variational Quantum Attacks
• Quantum nuclear dynamics on a distributed set of ion-trap quantum computing systems
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution
• Shaded tangles for the design and verification of quantum circuits
• Time-dependent variational principle for open quantum systems with artificial neural networks
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Effective spin physics in two-dimensional cavity QED arrays
• Quantum Coherence of Topologically Frustrated Spin Chains
• Dual-VQE: A quantum algorithm to lower bound the ground-state energy
• Bang-bang preparation of quantum many-body ground states in two dimensions: optimization of the algorithm with a two-dimensional tensor network
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Tensor-Programmable Quantum Circuits for Solving Differential Equations
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• Optimal bounds on the positivity of a matrix from a few moments
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Machine learning, quantum chaos, and pseudorandom evolution
• Quantum Gauge Networks: A New Kind of Tensor Network
• Optimization via Quantum Preconditioning
• Strictly local tensor networks for short-range topological insulators
• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Effects of electron-electron interactions in the Yu-Shiba-Rusinov lattice model
• Efficient tensor networks for control-enhanced quantum metrology
• The condition number of many tensor decompositions is invariant under Tucker compression
• Simulation of the Ring-exchange Models with Projected Entangled Pair States
• A quantum inspired approach to learning dynamical laws from data -- block-sparsity and gauge-mediated weight sharing
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit
• Scale-Invariant Continuous Entanglement Renormalization of a Chern Insulator
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Improved Matrix Product Operator Renormalization Group: application to the N-color random Ashkin-Teller chain
• Dynamics and Geometry of Entanglement in Many-Body Quantum Systems
• Stacked tree construction for free-fermion projected entangled pair states
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Redundant string symmetry-based error correction: Demonstrations on quantum devices
• Dynamical deconfinement transition driven by density of excitations
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• The Cytnx Library for Tensor Networks
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Adiabatic ground state preparation in an expanding lattice
• Nonlocal order parameter of pair superfluids
• Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics
• Accelerating Decision Diagram-based Multi-node Quantum Simulation with Ring Communication and Automatic SWAP Insertion
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm
• Optimal Qubit Mapping Search for Encoding Classical Data into Matrix Product State Representation with Minimal Loss
• Scaling of contraction costs for entanglement renormalization algorithms including tensor Trotterization and variational Monte Carlo
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Spectroscopic Feature of Quantum Many-Body Scar States
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Equivalence checking of quantum circuits via intermediary matrix product operator
• Gate-Based Initialization and Fidelity in Correlated Open Quantum Systems
• Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers
• Noise resilience in adaptive and symmetric monitored quantum circuits
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• A Parameter-Efficient Quantum Anomaly Detection Method on a Superconducting Quantum Processor
• Chemical master equation parameter exploration using DMRG
• Counterflow of lattice polarons in harmonically confined optical lattices
• Multiphoton, multimode state classification for nonlinear optical circuits
• Scalable projected entangled-pair state representation of random quantum circuit states
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• Auxiliary-Field Monte Carlo for lattice bosons: tackling strong interactions and frustration
• Typical Machine Learning Datasets as Low-Depth Quantum Circuits
• Chiral Gravitons on the Lattice
• Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC
• Analyzing the free states of one quantum resource theory as resource states of another
• Tangent Space Excitation Ansatz for Quantum Circuits
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Toolchain for Faster Iterations in Quantum Software Development
• Designing spin channel geometries for entanglement distribution
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Simulating Quantum Turbulence with Matrix Product States
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• An Extensible Quantum Network Simulator Built on ns-3: Q2NS Design and Evaluation
• Fermi Machine -- Quantum Many-Body Solver Derived from Correspondence between Noninteracting and Strongly Correlated Fermions
• Mode folding in systems with local interaction: unitary and non-unitary transformations using tensor states
• WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains
• Zero-site DMRG and the optimal low-rank correction
• Generalised ansatz for continuous Matrix Product States
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Efficient modeling of superconducting quantum circuits with tensor networks
• Dynamical symmetry in quantum dissipative models
• Variational boundary based tensor network renormalization group
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Interrelations among frustration-free models via Witten's conjugation
• Symmetrizing the Constraints -- Density Matrix Renormalization Group for Constrained Lattice Models
• Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
• Entanglement renormalization for quantum fields with boundaries and defects
• Finding the ground states of symmetric infinite-dimensional Hamiltonians: explicit constrained optimizations of tensor networks
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Implementing the sine transform of fermionic modes as a tensor network
• Tunable Magnetic Order in Chiral Coupled Spin Chains
• Inchworm tensor train hybridization expansion quantum impurity solver
• Numerically exact quantum dynamics with tensor networks: Predicting the decoherence of interacting spin systems
• Representation Theorem for Matrix Product States
• Variational optimization of projected entangled-pair states on the triangular lattice
• Optimal quantum reservoir learning in proximity to universality
• Snapshot spectra in the world-line quantum Monte Carlo for one-dimensional quantum spin systems
• Pushing Tensor Networks to the Limit
• Border Ranks of Positive and Invariant Tensor Decompositions: Applications to Correlations
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• ${\mathbb{Z}}_N$ symmetry breaking in Projected Entangled Pair State models
• Tensor Network Efficiently Representing Schmidt Decomposition of Quantum Many-Body States
• The infinite occupation number basis of bosons - solving a numerical challenge
• Single-layer framework of variational tensor network states
• Seeding neural network quantum states with tensor network states
• First-principle construction of U(1) symmetric matrix product states
• Holographic tensor network for double-scaled SYK
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
• Omnisolver: an extensible interface to Ising spin glass solvers
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Vertex Representation of Hyperbolic Tensor Networks
• Spectral Independence via Stability and Applications to Holant-Type Problems
• Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations
• Optimisation-Free Recursive QAOA for the Binary Paint Shop Problem
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Quantum-Inspired Tempering for Ground State Approximation using Artificial Neural Networks
• Fast Tensor Disentangling Algorithm
• Full- and low-rank exponential Euler integrators for the Lindblad equation
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Entanglement transitions in a boundary-driven open quantum many-body system
• Optimal sampling of tensor networks targeting wave function's fast decaying tails
• Efficient approximation for global functions of matrix product operators
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• Symmetries and field tensor network states
• The Software Landscape for the Density Matrix Renormalization Group
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• QAS-QTNs: Curriculum Reinforcement Learning-Driven Quantum Architecture Search for Quantum Tensor Networks
• Harnessing spin-qubit decoherence to probe strongly-interacting quantum systems
• Bulk-edge correspondence in the Haldane phase of the bilinear-biquadratic spin-1 Hamiltonian
• On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain
• Extracting Coupling-Mode Spectral Densities with Two-Dimensional Electronic Spectroscopy
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• Two-stage melting of an inter-component Potts long-range order in two dimensions
• A Hermitian bypass to the non-Hermitian quantum theory
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Deformations of the Boundary Theory of the Square Lattice AKLT Model
• Quantum max-flow in the bridge graph
• Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Tensor Network Estimation of Distribution Algorithms
• Limits of Clifford Disentangling in Tensor Network States
• Entanglement scaling and criticality of infinite-size quantum many-body systems in continuous space addressed by a tensor network approach
• Logarithmic growth of operator entanglement in a clean non-integrable circuit
• The product structure of MPS-under-permutations
• Grassmann tensor networks
• Frustration-induced degenerate spin state with up-up-down-down ordering in corner-connected Heisenberg square-plaquettes
• Characterizing quantum phase transition by teleportation
• On the geometry of Tensor Network States of $2\times N$ Grids
• A Shielding Property for Thermal Equilibrium States on the Quantum Ising Model
• Symmetry-enforced minimal entanglement and correlation in quantum spin chains
• Using matrix-product states for time-series machine learning
• Learning a compass spin model with neural network quantum states
• Faster randomized partial trace estimation
• Information Bounds on phase transitions in disordered systems
• Tensorization of neural networks for improved privacy and interpretability
• Quantum Entanglement of Anyonic Charges and Emergent Spacetime Geometry
• Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method
• The Canonical Forms of Matrix Product States in Infinite-Dimensional Hilbert Spaces
• Dynamical cluster-based strategy for improving tensor network algorithms in quantum circuit simulations
• Principle of learning sign rules by neural networks in qubit lattice models
• Energy of fermionic ground states with low-entanglement single-reference expansions, and tensor-based strong-coupling extensions of the coupled-cluster method
• Variational decision diagrams for quantum-inspired machine learning applications
• Quantum Computing Solution of the Bethe-Salpeter Equation for Relativistic Scalar Bound States via Tensor-Network VQE
• Quantum Encoding of Structured Data with Matrix Product States
• Dynamical quantum phase transitions on random networks
• Tight and self-testing multipartite quantum Bell inequalities from the renormalization group
• Self-interacting processes via Doob conditioning
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• A Graphical #SAT Algorithm for Formulae with Small Clause Density
• Solving the time-independent Schrödinger equation for chains of coupled excitons and phonons using tensor trains
• Bell sampling in Quantum Monte Carlo simulations
• Explaining Anomalies with Tensor Networks
• Quantum non-Markovianity elusive to interventions
• TTNOpt: Tree tensor network package for high-rank tensor compression
• The Gauge Picture of Quantum Dynamics
• Entanglement entropy of two-species hard-core bosons in one dimension
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
• Entanglement structure for finite system under dual-unitary dynamics
• One-dimensional interacting Su-Schrieffer-Heeger model at quarter filling: An exact diagonalization study
• Tensor Train Quantum State Tomography using Compressed Sensing
• Matrix-product entanglement characterizing the optimality of state-preparation quantum circuits
• Beyond Ground States: Physics-Inspired Optimization of Excited States of Classical Hamiltonians
• Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model
• Dimerization of many-body subradiant states in waveguide quantum electrodynamics
• Fractal Path Strategies for Efficient 2D DMRG Simulations
• Truncating loopy tensor networks by zero-mode gauge fixing
• Electronic correlations in magnetized helical edge states coupled to s-wave superconductors
• Improving the performance of fermionic neural networks with the Slater exponential Ansatz
• Preparation of the single-spinon wave function on a quantum computer
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
• A penalty-free quantum algorithm to find energy eigenstates
• Time evolution of controlled many-body quantum systems with matrix product operators
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• A Study on Stabilizer Rényi Entropy Estimation using Machine Learning
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Half-Chain Entanglement Entropy in the One-Dimensional Spinless Fermion Model
• Tensor-Network study of Ising model on infinite hyperbolic dodecahedral lattice
• Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
• Resource complexity of Symmetry Protected Topological phases
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
• Continuous matrix product operators for quantum fields
• Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition
• Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems
• Tensor Network Lattice Boltzmann Method for Data-Compressed Fluid Simulations
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Variational matrix product states for combinatorial optimization
• Phase structure of the one-dimensional ${\mathbb{Z}}_2$ lattice gauge theory with second nearest-neighbor interactions
• Stability of the symmetry-protected topological phase and Ising transitions in a disordered U(1) quantum link model on a ladder
• Who can compete with quantum computers? Lecture notes on quantum inspired tensor networks computational techniques
• Gapless deconfined phase in a ${\mathbb{Z}}_N$ symmetric Hamiltonian created in a cold-atom setup
• Emulation of large-scale qubit registers with a phase-space approach
• Sampling two-dimensional isometric tensor network states
• Simulation of the Dissipative Dynamics of Strongly Interacting NV Centers with Tensor Networks
• Leaf-to-leaf distances in Catalan trees
• Variational Quantum Algorithm Landscape Reconstruction by Low-Rank Tensor Completion
• Optimization of Quantum Systems Emulation via a Variant of the Bandwidth Minimization Problem
• Time series generation for option pricing on quantum computers using tensor network