Tensor networks for complex quantum systems

Abstract

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory and the understanding of entanglement in quantum many-body systems. Moreover, it has been not-so-long realized that tensor network states play a key role in other scientific disciplines, such as quantum gravity and artificial intelligence. In this context, here we provide an overview of basic concepts and key developments in the field. In particular, we briefly discuss the most important tensor network structures and algorithms, together with a sketch on advances related to global and gauge symmetries, fermions, topological order, classification of phases, entanglement Hamiltonians, AdS/CFT, artificial intelligence, the 2d Hubbard model, 2d quantum antiferromagnets, conformal field theory, quantum chemistry, disordered systems, and many-body localization.

16 pages, 6 figures, 1 table, 1 technical box. Revised version for arXiv. Final version (with minor style modifications) to appear in Nature Reviews Physics

References in corpus (39)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Area laws in quantum systems: mutual information and correlations
• 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
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• Scaling of entanglement support for Matrix Product States
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• Continuous Matrix Product States for Quantum Fields
• Robustness of a perturbed topological phase
• Matrix Product States for dynamical simulation of infinite chains
• Applying matrix product operators to model systems with long-range interactions
• Entanglement renormalization and topological order
• Variational quantum Monte Carlo simulations with tensor-network states
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• Explicit tensor network representation for the ground states of string-net models
• Strings, Projected Entangled Pair States, and variational Monte Carlo methods
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Entanglement renormalization and gauge symmetry
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Chebyshev Matrix Product State Impurity Solver for the Dynamical Mean-Field Theory
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• Spectral tensor networks for many-body localization
• Simulation of anyons with tensor network algorithms
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Fermionic projected entangled-pair states and topological phases
• Rigorous free fermion entanglement renormalization from wavelet theory
• Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition
• Tensor-product representations for string-net condensed states
• Entanglement Continuous Unitary Transformations

Cited by in corpus (343)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Recurrent Neural Network Wave Functions
• Is there evidence for exponential quantum advantage in quantum chemistry?
• Simulation methods for open quantum many-body systems
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Machine Learning for Quantum Matter
• Many-Body Localization in the Age of Classical Computing
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks
• Quantum autoencoders to denoise quantum data
• Neural tensor contractions and the expressive power of deep neural quantum states
• Neural network wave functions and the sign problem
• Quantum simulation with hybrid tensor networks
• Unified approach to data-driven quantum error mitigation
• An end-to-end trainable hybrid classical-quantum classifier
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Barren plateaus in quantum tensor network optimization
• Entanglement barrier and its symmetry resolution: theory and experiment
• Breaking the entanglement barrier: Tensor network simulation of quantum transport
• Variational Benchmarks for Quantum Many-Body Problems
• Toward Practical Quantum Embedding Simulation of Realistic Chemical Systems on Near-term Quantum Computers
• Efficient Tensor Network ansatz for high-dimensional quantum many-body problems
• Efficient tensor network simulation of IBM's largest quantum processors
• X-Symbols for Non-Abelian Symmetries in Tensor Networks
• Tensor Network Python (TeNPy) version 1
• Multiloop functional renormalization group approach to quantum spin systems
• The learnability scaling of quantum states: restricted Boltzmann machines
• Sequential generation of projected entangled-pair states
• Optimizing Design Choices for Neural Quantum States
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Two-dimensional quantum-link lattice Quantum Electrodynamics at finite density
• Complexity of frustration: a new source of non-local non-stabilizerness
• Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
• Probabilistic Nonunitary Gate in Imaginary Time Evolution
• Tensor network representations of parton wave functions
• Multi-class quantum classifiers with tensor network circuits for quantum phase recognition
• Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks
• Accurate simulation for finite projected entangled pair states in two dimensions
• Tensor networks for quantum machine learning
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Fermionic systems for quantum information people
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Characterizing entanglement dimensionality from randomized measurements
• Ollivier-Ricci curvature convergence in random geometric graphs
• Grammar-aware sentence classification on quantum computers
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Automatic structural optimization of tree tensor networks
• Non-equilibrium phase transitions in $(1+1)$-dimensional quantum cellular automata with controllable quantum correlations
• Quantum many-body systems in thermal equilibrium
• Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data
• Tree tensor network classifiers for machine learning: from quantum-inspired to quantum-assisted
• Gauging tensor networks with belief propagation
• Rényi Entropy Singularities as Signatures of Topological Criticality in Coupled Photon-Fermion Systems
• Tensor networks enable the calculation of turbulence probability distributions
• Generative machine learning with tensor networks: benchmarks on near-term quantum computers
• Predicting quantum dynamical cost landscapes with deep learning
• Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems
• Tensor-network study of correlation-spreading dynamics in the two-dimensional Bose-Hubbard model
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Plasmonic Purcell Effect in Organic Molecules
• Projection algorithm for state preparation on quantum computers
• Variational autoencoder reconstruction of complex many-body physics
• Hyper-optimized approximate contraction of tensor networks with arbitrary geometry
• Finite time large deviations via matrix product states
• Many-Body Quantum States with Exact Conservation of Non-Abelian and Lattice Symmetries through Variational Monte Carlo
• Characterizing quantum correlations in spin chains
• On Quantum Gravity If Non-Locality Is Fundamental
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• Optimal sampling of dynamical large deviations via matrix product states
• Particle-hole asymmetry in the dynamical spin and charge structure factors of the corner-shared one-dimensional cuprates
• Reconstructing complex states of a 20-qubit quantum simulator
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Automatically Differentiable Quantum Circuit for Many-qubit State Preparation
• Adaptive-weighted tree tensor networks for disordered quantum many-body systems
• Competing quantum phases of hard-core boson with tilted dipole-dipole interaction
• Magnetization of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice
• Continuous matrix product operator approach to finite temperature quantum states
• A variational approach for many-body systems at finite temperature
• Quantum variational learning for quantum error-correcting codes
• Time-dependent variational principle with controlled bond expansion for matrix product states
• Tensor networks for interpretable and efficient quantum-inspired machine learning
• Hilbert space delocalization under random unitary circuits
• Generating Function for Tensor Network Diagrammatic Summation
• Augmenting Density Matrix Renormalization Group with Disentanglers
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Critical analysis of two-dimensional classical XY model
• Entanglement accelerates quantum simulation
• Entanglement bipartitioning and tree tensor networks
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Variational Quantum Optimization of Nonlocality in Noisy Quantum Networks
• Tensor networks for quantum computing
• Opening the Black Box Inside Grover's Algorithm
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Asymptotic survival of genuine multipartite entanglement in noisy quantum networks depends on the topology
• Variational Quantum Eigensolver for SU($N$) Fermions
• Numerical linked cluster expansions for inhomogeneous systems
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Quantum algorithms for scientific computing
• TeNeS: Tensor Network Solver for Quantum Lattice Systems
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• QuantumToolbox.jl: An efficient Julia framework for simulating open quantum systems
• Weak first-order phase transitions in the frustrated square lattice J1-J2 classical Ising model
• Block belief propagation algorithm for two-dimensional tensor networks
• Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variations
• Symbolic Execution for Quantum Error Correction Programs
• Bias-Field Digitized Counterdiabatic Quantum Algorithm for Higher-Order Binary Optimization
• Loop-Free Tensor Networks for High-Energy Physics
• Neural Projected Quantum Dynamics: a systematic study
• Multipartite correlations in quantum collision models
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Unifying view of fermionic neural network quantum states: From neural network backflow to hidden fermion determinant states
• Symmetric Tensor Networks for Generative Modeling and Constrained Combinatorial Optimization
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Validating quantum-supremacy experiments with exact and fast tensor network contraction
• Quantum Computing and Tensor Networks for Laminate Design: A Novel Approach to Stacking Sequence Retrieval
• Tensor-network-assisted variational quantum algorithm
• Conformal Properties of Hyperinvariant Tensor Networks
• Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators
• Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound
• Variational corner transfer matrix renormalization group method for classical statistical models
• Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer
• Probing critical states of matter on a digital quantum computer
• Dynamical quantum phase transitions in the one-dimensional extended Fermi-Hubbard model
• Benchmarking global $SU(2)$ symmetry in 2d tensor network algorithms
• Primordial Gravitational Wave Circuit Complexity
• Nonstabilizerness dynamics in many-body localized systems
• Estimating the randomness of quantum circuit ensembles up to 50 qubits
• Fine-Grained Tensor Network Methods
• Numerical Simulation of Critical Quantum Dynamics without Finite Size Effects
• Functional Tensor Network Solving Many-body Schrödinger Equation
• A tensor network discriminator architecture for classification of quantum data on quantum computers
• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• Mixed states in one spatial dimension: decompositions and correspondence with nonnegative matrices
• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• Adaptive projected variational quantum dynamics
• Dynamics of correlation spreading in low-dimensional transverse-field Ising models
• Deep learning Local Reduced Density Matrices for Many-body Hamiltonian Estimation
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Adaptive variational low-rank dynamics for open quantum systems
• Quantum many-body simulations with PauliStrings.jl
• Thermal bosons in 3d optical lattices via tensor networks
• Hybrid Tree Tensor Networks for quantum simulation
• Scalable Imaginary Time Evolution with Neural Network Quantum States
• From edge to bulk: Cavity induced displacement of topological non-local qubits
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• The seniority quantum number in Tensor Network States
• More on symmetry resolved operator entanglement
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Efficient calculation of three-dimensional tensor networks
• TorchQC -- A framework for efficiently integrating machine and deep learning methods in quantum dynamics and control
• Field-induced Bose-Einstein condensation and supersolid in the two-dimensional Kondo necklace
• Thermalization in Kitaev's quantum double models via Tensor Network techniques
• Tensor network renormalization group study of spin-1 random Heisenberg chains
• Continuous ferromagnetic quantum phase transition on an anisotropic Kondo lattice
• NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians
• Explainable Natural Language Processing with Matrix Product States
• Tensor Networks for Explainable Machine Learning in Cybersecurity
• Tensor network decompositions for absolutely maximally entangled states
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Fermionic Magic Resources of Quantum Many-Body Systems
• Exactly solvable models for universal operator growth
• Sampling diverse near-optimal solutions via algorithmic quantum annealing
• Fractional resonances and prethermal states in Floquet systems
• Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
• Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
• Fuzzy measurements and coarse graining in quantum many-body systems
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• Random Sampling Neural Network for Quantum Many-Body Problems
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Tensorized orbitals for computational chemistry
• Simulator Demonstration of Large Scale Variational Quantum Algorithm on HPC Cluster
• Detecting emergent continuous symmetries at quantum criticality
• Classical spin Hamiltonians are context-sensitive languages
• Quantum mean estimation for lattice field theory
• Disentangling magic states with classically simulable quantum circuits
• Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps
• Pseudo-fermion functional renormalization group with magnetic fields
• Statistical Mechanics Approach to the Holographic Renormalization Group: Bethe Lattice Ising Model and p-adic AdS/CFT
• Capturing long-range memory structures with tree-geometry process tensors
• Stack operation of tensor networks
• TNQMetro: Tensor-network based package for efficient quantum metrology computations
• Holographic analysis of boundary correlation functions for the hyperbolic-lattice Ising model
• Topological dualities via tensor networks
• Bosonic entanglement renormalization circuits from wavelet theory
• Language Modeling with Reduced Densities
• Tensor-network approach to thermalization in open quantum many-body systems
• Computing quantum magic of state vectors
• Active quantum flocks
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Loop Series Expansions for Tensor Networks
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Quantum computing for simulation of fluid dynamics
• Quantum computing quantum Monte Carlo algorithm
• Bell non-locality using tensor networks and sparse recovery
• Fermionic tensor network contraction for arbitrary geometries
• Generation of photonic tensor network states with Circuit QED
• Single-layer tensor network approach for three-dimensional quantum systems
• The resource theory of tensor networks
• Correlated states in super-moiré materials with a kernel polynomial quantics tensor cross interpolation algorithm
• Field Tensor Network States
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Matrix-product unitaries: Beyond quantum cellular automata
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Efficient simulation of inhomogeneously correlated systems using block interaction product states
• Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
• Equivariant Tensor Network Potentials
• Variational Tensor Network Operator
• Emergent Quantum Mechanics at the Boundary of a Local Classical Lattice Model
• Unveiling clean two-dimensional discrete time crystals on a digital quantum computer
• Tensor-Network Approaches to Counting Statistics for the Current in a Boundary-Driven Diffusive System
• Machine Learning Wavefunction
• Sequential quantum simulation of spin chains with a single circuit QED device
• Relationship between the ground-state wave function of a magnet and its static structure factor
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• H-wave -- A Python package for the Hartree-Fock approximation and the random phase approximation
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Spin correlations in the bilayer Hubbard model with perpendicular electric field
• Image Classification by Throwing Quantum Kitchen Sinks at Tensor Networks
• Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary
• Large-scale stochastic simulation of open quantum systems
• Controlling quantum many-body systems using reduced-order modelling
• A Matrix Product State Model for Simultaneous Classification and Generation
• Hamiltonian Learning of Triplon Excitations in an Artificial Nanoscale Molecular Quantum Magnet
• Unifying O(3) Equivariant Neural Networks Design with Tensor-Network Formalism
• Quantum natural gradient without monotonicity
• Stable many-body resonances in open quantum systems
• Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model
• qlbm -- A Quantum Lattice Boltzmann Software Framework
• Hamiltonian-learning quantum magnets with non-local impurity tomography
• Constructive Fermionic Matrix Product States for Projected Fermi Sea
• Survey on Computational Applications of Tensor Network Simulations
• Continuous monitoring for noisy intermediate-scale quantum processors
• Quantum Coherence of Topologically Frustrated Spin Chains
• Achieving the volume-law entropy regime with random-sign Dicke states
• Neural Quantum State Study of Fracton Models
• Quantum Gauge Networks: A New Kind of Tensor Network
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm
• Polynomial decompositions with invariance and positivity inspired by tensors
• Tensor Decompositions and Adiabatic Quantum Computing for Discovering Practical Matrix Multiplication Algorithms
• Multiphoton, multimode state classification for nonlinear optical circuits
• Valence-Bond Solid phases in the spin-$1/2$ Kekule-Heisenberg model
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Mott Transition and Volume Law Entanglement with Neural Quantum States
• Entanglement-informed Construction of Variational Quantum Circuits
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• Scalable projected entangled-pair state representation of random quantum circuit states
• Simple Fermionic backflow states via a systematically improvable tensor decomposition
• Quantum tensor network algorithms for evaluation of spectral functions on quantum computers
• Chemical master equation parameter exploration using DMRG
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• Exploring the Nexus between Thermodynamic Phase Transitions and Geometric Fractals through Systematic Lattice Point Classification
• Improving accuracy of tree-tensor network approach by optimization of network structure
• The Cytnx Library for Tensor Networks
• Simulation of the 1d XY model on a quantum computer
• Ab-Initio Approach to Many-Body Quantum Spin Dynamics
• Improving neural network performance for solving quantum sign structure
• Tensor Network for Anomaly Detection in the Latent Space of Proton Collision Events at the LHC
• Hardness-dependent quantum adiabatic schedules for the maximum-independent-set problem
• Tangent Space Excitation Ansatz for Quantum Circuits
• Field digitization scaling in a ${\mathbb{Z}}_N\subset U(1)$ symmetric model
• Universal scaling laws in quantum-probabilistic machine learning by tensor network towards interpreting representation and generalization powers
• Positive bias makes tensor-network contraction tractable
• Optimal Qubit Mapping Search for Encoding Classical Data into Matrix Product State Representation with Minimal Loss
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Generalised ansatz for continuous Matrix Product States
• Exploiting many-body localization for scalable variational quantum simulation
• Vertex Representation of Hyperbolic Tensor Networks
• The Tensor as an Informational Resource
• A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas
• Floquet Schrieffer-Wolff transform based on Sylvester equations
• Exact average many-body interatomic interaction model for random alloys
• A Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics
• Quantum max-flow in the bridge graph
• Quick design of feasible tensor networks for constrained combinatorial optimization
• A Lindbladian for exact renormalization of density operators in QFT
• Hidden quantum correlations in the ground states of quasiclassical spin systems
• Competing pair density wave orders in the square lattice $t$-$J$ model
• Short-time simulation of quantum dynamics by Pauli measurements
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states
• Blockwise Optimization for Projective Variational Quantum Dynamics (BLOP-VQD): Algorithm and Implementation for Lattice Systems
• Revealing quantum phase string effect in doped Mott-insulator: a tensor network state approach
• Improving Variational Counterdiabatic Driving with Weighted Actions and Computer Algebra
• Seeding neural network quantum states with tensor network states
• Fast Tensor Disentangling Algorithm
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• The Bayesian Method of Tensor Networks
• The Software Landscape for the Density Matrix Renormalization Group
• Quantum Fisher information from tensor network integration of Lyapunov equation
• Variational boundary based tensor network renormalization group
• Integrability and scattering of the boson field theory on a lattice
• Artificial intelligence for representing and characterizing quantum systems
• Variational optimization of projected entangled-pair states on the triangular lattice
• Bound on entanglement in neural quantum states
• Single-layer framework of variational tensor network states
• Approximate tensor decompositions: disappearance of many separations
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Ground-state phase diagram of the SU($4$) Heisenberg model on a plaquette lattice
• Second Rényi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries
• Quasi-adiabatic thermal ensemble preparation in the thermodynamic limit
• Magnetization of electronic ground states in frustrated superstable graphs
• Quantendynamik offener Systeme, Trendbericht Theoretische Chemie 2020, Teil 3
• Holographic Aspects of Dynamical Mean-Field Theory
• Intrinsic Step Jamming in Nanometer-Scale KPZ-like Rough Surfaces under Interface-Limited Crystal Growth and Retreat
• Programmable order by disorder effect and underlying phases through dipolar quantum simulators
• Mott-insulating phases of the Bose-Hubbard model on quasi-1D ladder lattices
• Finite graphs and configurations of points
• Limits of Clifford Disentangling in Tensor Network States
• Grassmann tensor networks
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Energy Spectra of Compressed Quantum States
• 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
• Accelerated spin-adapted ground state preparation with non-variational quantum algorithms
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
• TTNOpt: Tree tensor network package for high-rank tensor compression
• Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks
• Certification of spin-based quantum simulators
• Benchmarking quantum devices beyond classical capabilities
• Faster randomized partial trace estimation
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
• Quantum Compressive Sensing: Mathematical Machinery, Quantum Algorithms, and Quantum Circuitry
• Computable and noncomputable in the quantum domain: statements and conjectures
• Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection
• Degeneracy Engineering for Classical and Quantum Annealing: A Case Study of Sparse Linear Regression in Collider Physics
• Bayesian inference of general noise-model parameters from the syndrome statistics of surface codes
• Learning Minimal Representations of Fermionic Ground States
• High-precision ground state parameters of the two-dimensional spin-1/2 Heisenberg model on the square lattice
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• Information geometry of nonmonotonic quantum natural gradient