Time-evolution methods for matrix-product states

Abstract

Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a matrix-product state. Here, we will review and summarize the recent work on this topic as applied to finite quantum systems. We will explain and compare the different methods available to construct a time-evolved matrix-product state, namely the time-evolving block decimation, the MPO $W^{\mathrm{II}}$ method, the global Krylov method, the local Krylov method and the one- and two-site time-dependent variational principle. We will also apply these methods to four different representative examples of current problem settings in condensed matter physics.

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• Qubit-oscillator relationships in the open quantum Rabi model: the role of dissipation
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Dynamical quantum phase transition and thermal equilibrium in the lattice Thirring model
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Non-linear classification capability of quantum neural networks due to emergent quantum metastability
• Moment method and continued fraction expansion in Floquet Operator Krylov Space
• More on the Operator Space Entanglement (OSE): Rényi OSE, revivals, and integrability breaking
• Cold atoms meet lattice gauge theory
• Probing Green's Function Zeros by Co-tunneling through Mott Insulators
• Dynamical Phase Error in Interacting Topological Quantum Memories
• Twin-Space Representation of Classical Mapping Model in the Constraint Phase Space Representation: Numerically Exact Approach to Open Quantum Systems
• Fully numerical Hartree-Fock calculations for atoms and small molecules with quantics tensor trains
• Quantum transport phenomena induced by time-dependent fields
• Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm
• Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
• Spreading of a local excitation in a Quantum Hierarchical Model
• Simulating Quantum Turbulence with Matrix Product States
• Gate-Based Initialization and Fidelity in Correlated Open Quantum Systems
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Pseudogap with Fermi arcs and Fermi pockets in half-filled twisted transition metal dichalcogenides
• Influence functional of many-body systems: temporal entanglement and matrix-product state representation
• Phonon state tomography of electron correlation dynamics in optically excited solids
• Equivalence checking of quantum circuits via intermediary matrix product operator
• Quantum phase transition in the one-dimensional Dicke-Hubbard model with coupled qubits
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Measuring temporal entropies in experiments
• A Quantum-Inspired Algorithm for Wave Simulation Using Tensor Networks
• Extracting the spin excitation spectrum of a fermionic system using a quantum processor
• Propagation of two-particle correlations across the chaotic phase for interacting bosons
• Approximate Contraction of Arbitrary Tensor Networks with a Flexible and Efficient Density Matrix Algorithm
• Matrix-product-state-based band-Lanczos solver for quantum cluster approaches
• Chiral Gravitons on the Lattice
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• WaveTrain: A Python Package for Numerical Quantum Mechanics of Chain-Like Systems Based on Tensor Trains
• Two-beam Multiparticle Many-body simulations of Inhomogeneous FFI
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Time evolution of the local density of states of strongly correlated fermions coupled to a nanoprobe
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
• Stability of Floquet sidebands and quantum coherence in 1D strongly interacting spinless fermions
• Spectroscopy and complex-time correlations using minimally entangled typical thermal states
• Quantum Fisher information as a witness of non-Markovianity and criticality in the spin-boson model
• Determining probability density functions with adiabatic quantum computing
• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
• $\nu$-QSSEP: A toy model for entanglement spreading in stochastic diffusive quantum systems
• Impact of Loss Mechanisms on Linear Spectra of Excitonic and Polaritonic Aggregates
• Thermal Drude weight in an integrable chiral clock model
• Symmetry- and energy-resolved entanglement dynamics in a disordered Bose-Hubbard model
• Provably Efficient Simulation of 1D Long-Range Interacting Systems at Any Temperature
• Emergence of topological states in relaxation dynamics of interacting bosons
• The Software Landscape for the Density Matrix Renormalization Group
• Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers
• The ITransverse.jl library for transverse tensor network contractions
• Spin Seebeck effect of interacting spinons
• Kondo nanomechanical dissipation in the driven Anderson impurity model
• Variational approach to open quantum systems with long-range competing interactions
• Chain-mapping methods for relativistic light-matter interactions
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Learning out-of-time-ordered correlators with classical kernel methods
• Realization of Two-dimensional Discrete Time Crystals with Anisotropic Heisenberg Coupling
• A coherent approach to quantum-classical optimization
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Emergent Pair Density Wave Order Across a Lifshitz Transition
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Classical restrictions of generic matrix product states are quasi-locally Gibbsian
• Temperature dependence of energy transport in the ${\mathbb{Z}}_3$ chiral clock model
• High-temperature partition functions and classical simulatability of long-range quantum systems
• Robustness of near-thermal dynamics on digital quantum computers
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Hartree-Fock approximation for bosons with symmetry-adapted variational wave functions
• Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network
• Quasi-Fermi liquid behavior in a one-dimensional system of interacting spinless fermions
• Integrals of motion as slow modes in dissipative many-body operator dynamics
• Pseudospectral method for solving PDEs using Matrix Product States
• Stability of thermal equilibrium in long-range quantum systems
• Tensor network method for real-space topology in quasicrystal Chern mosaics
• Scaling up the transcorrelated density matrix renormalization group
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Ferromagnetism and doublon localization in a Wannier-Hubbard chain
• Quantum Magnetic Skyrmions on Kondo-type Lattices
• Locally accurate tensor networks for thermal states and time evolution
• Possibility to detect the bound state of the Heisenberg ferromagnetic chain at intermediate temperature
• Charge density wave breakdown in a heterostructure with electron-phonon coupling
• Pauli weight requirement of the matrix elements in time-evolved local operators: dependence beyond the equilibration temperature
• Transport in a System with a Tower of Quantum Many-Body Scars
• Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
• Dynamical quantum phase transitions on random networks
• Near-Term Fermionic Simulation with Subspace Noise Tailored Quantum Error Mitigation
• Adaptive Kink Filtration: Achieving Asymptotic Size-Independence of Path Integral Simulations Utilizing the Locality of Interactions
• Skyrmionic Schrödinger cat states in monoaxial chiral magnets
• Emergent spinon-holon Feshbach resonance in a doped Majumdar-Ghosh model
• Data-Driven Time Propagation of Quantum Systems with Neural Networks
• Simulation of the Dissipative Dynamics of Strongly Interacting NV Centers with Tensor Networks
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
• Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra
• Quantum typicality approach to energy flow between two spin-chain domains at different temperatures
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems
• Geometrically Taming Dynamical Entanglement Growth in Purified Quantum States
• Matrix product states and first quantization
• Time evolution of controlled many-body quantum systems with matrix product operators
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Dissipative Generation of Currents by Nonreciprocal Local and Global Environments
• Resource complexity of Symmetry Protected Topological phases
• Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Quantum simulation in the entanglement picture
• Dynamical Tensor Train Approximation for Kinetic Equations
• Integral formula for the propagator of the one-dimensional Hubbard model
• Rate Function Modelling of Quantum Many-Body Adiabaticity
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
• Bound-state confinement after trap-expansion dynamics in integrable systems
• Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics
• Dynamically generated quadrupole polarization using Floquet adiabatic evolution
• Persistent-current states originating from the Hilbert space fragmentation in momentum space
• Effect of Temperature Gradient on Quantum Transport
• Dynamics of Interacting Bosons on the Sawtooth Lattice with a Flat Band
• Fate of Bosonic Topological Edge Modes in the Presence of Many-Body Interactions
• Many-body localization in a tilted potential in two dimensions
• A Thermofield-based Multilayer Multiconfigurational Time-Dependent Hartree Approach to Non-Adiabatic Quantum Dynamics at Finite Temperature
• Nonequilibrium dark space phase transition
• Localization dynamics in a centrally coupled system
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach
• Variational Tensor Network Simulation of Gaussian Boson Sampling and Beyond