For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
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Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
34 Pith papers cite this work. Polarity classification is still indexing.
34
Pith papers citing it
abstract
We describe quantum many--body systems in terms of projected entangled--pair states, which naturally extend matrix product states to two and more dimensions. We present an algorithm to determine correlation functions in an efficient way. We use this result to build powerful numerical simulation techniques to describe the ground state, finite temperature, and evolution of spin systems in two and higher dimensions.
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background 4representative citing papers
Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
A Set-Transformer architecture with self-attention encodes Pauli-string correlations, optimizes via commutation objective, and finds symmetries with near-deterministic success on physical models like Ising and Toric code.
A zero-mode gauge fixing technique truncates bonds in loopy tensor networks by exploiting linear dependencies in the metric tensor of cut-bond states, applied to iPEPS representations of the finite-temperature 2D Z2 lattice gauge theory.
SCALE and ACE are new convolutional backflow architectures for Neural Quantum States that deliver O(N^3) scaling with high accuracy and over 40x speedup on Hubbard and t-J models up to 32x32 lattices.
A gauge-covariant PEPS ansatz with virtual flux tensors ensures translation-invariant physical expectation values for 2D interacting systems in a magnetic field, allowing gauge-independent simulations without enlarged magnetic unit cells.
Holographic isoTNS represent volume-law entangled states including arbitrary fermionic Gaussian states, Clifford states, and certain short-time evolved states using an extra network dimension with isometric constraints.
A technique extracts k-local conserved operators from iPEPS by identifying vanishing fidelity susceptibility in a quantum geometry of parameter-deformed states, yielding improved parent Hamiltonians for RVB and deformed toric code states.
iPEPS simulations with bond-dimension extrapolation locate a quantum spin liquid phase in the Shastry-Sutherland model for 0.785(5) ≤ J'/J ≤ 0.82(1).
TI MPS with permutational symmetry (entanglement similar across bipartitions) are shown to be trivial (product states or few superpositions); extends to generic MPS and states like W and Dicke approximately.
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.
Engineered local Hamiltonian controls in Rydberg arrays accelerate adiabatic convergence to MIS solutions, raise success probabilities over global controls, and cut fidelity decay rate by 25% as graphs harden.
Trotter error cancellation in nanographene simulations reduces circuit depth by about 10x for quantum phase estimation of energy gaps to chemical accuracy in the Pariser-Parr-Pople model.
A mean-field phase-space method emulates continuous-time dynamics of up to thousands of qubits with quadratic cost, capturing single-qubit observables qualitatively on transverse-field Ising models.
A single-layer variational tensor network method reduces computational cost by three orders of magnitude in bond dimension for 2D quantum models and confirms an intermediate empty-plaquette valence bond solid phase in the Shastry-Sutherland model.
NN-fTNS enhance fermionic tensor networks with neural parametrization to improve expressivity and achieve order-of-magnitude better energies than pure fTNS on Hubbard models while maintaining linear scaling.
The thesis introduces a topology-aware tensor-network heuristic called SpinGlassPEPS.jl and thermodynamic metrics to benchmark quantum annealers on Ising problems while accounting for dissipation and effective temperature.
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
A QR-based CTMRG variant accelerates iPEPS contractions by up to two orders of magnitude on GPUs with no accuracy loss for the Heisenberg and J1-J2 models.
In a star network of qubits with XYZ Heisenberg interactions, localizable bipartite peripheral entanglement grows logarithmically with periphery size at zero xy-anisotropy and survives noisy measurements in the large-periphery limit.
Numerical tensor-network study identifies Néel, Ising, collinear, and incommensurate spiral phases plus their transitions in the J1-J2 XY antiferromagnet on the honeycomb lattice.
citing papers explorer
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Algorithmic Locality via Provable Convergence in Quantum Tensor Networks
For PEPS with strong injectivity above a threshold, belief propagation finds fixed points efficiently and cluster-corrected BP approximates observables to 1/poly(N) error in poly(N) time, with local perturbations affecting the fixed point only locally.
-
Coherent-State Propagation: A Computational Framework for Simulating Bosonic Quantum Systems
Coherent-state propagation enables quasi-polynomial classical simulation of bosonic circuits with logarithmically many Kerr gates at exponentially small trace-distance error, with polynomial runtime in the weak-nonlinearity regime.
-
Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
For PEPS states with loop-decay, BP with cluster corrections approximates local observables exponentially accurately, and loop-decay necessarily implies exponential decay of connected correlations, ruling out BP at critical points.
-
Attention-based optimizer for symmetry finding
A Set-Transformer architecture with self-attention encodes Pauli-string correlations, optimizes via commutation objective, and finds symmetries with near-deterministic success on physical models like Ising and Toric code.
-
Truncating loopy tensor networks by zero-mode gauge fixing: the $Z_2$ lattice gauge theory at finite temperature
A zero-mode gauge fixing technique truncates bonds in loopy tensor networks by exploiting linear dependencies in the metric tensor of cut-bond states, applied to iPEPS representations of the finite-temperature 2D Z2 lattice gauge theory.
-
Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions
SCALE and ACE are new convolutional backflow architectures for Neural Quantum States that deliver O(N^3) scaling with high accuracy and over 40x speedup on Hubbard and t-J models up to 32x32 lattices.
-
Gauge-covariant projected entangled paired states for interacting systems in a magnetic field
A gauge-covariant PEPS ansatz with virtual flux tensors ensures translation-invariant physical expectation values for 2D interacting systems in a magnetic field, allowing gauge-independent simulations without enlarged magnetic unit cells.
-
Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks
Holographic isoTNS represent volume-law entangled states including arbitrary fermionic Gaussian states, Clifford states, and certain short-time evolved states using an extra network dimension with isometric constraints.
-
Extracting conserved operators from a projected entangled pair state
A technique extracts k-local conserved operators from iPEPS by identifying vanishing fidelity susceptibility in a quantum geometry of parameter-deformed states, yielding improved parent Hamiltonians for RVB and deformed toric code states.
-
Quantum spin liquid phase in the Shastry-Sutherland model revealed by high-precision infinite projected entangled-pair states
iPEPS simulations with bond-dimension extrapolation locate a quantum spin liquid phase in the Shastry-Sutherland model for 0.785(5) ≤ J'/J ≤ 0.82(1).
-
The product structure of MPS-under-permutations
TI MPS with permutational symmetry (entanglement similar across bipartitions) are shown to be trivial (product states or few superpositions); extends to generic MPS and states like W and Dicke approximately.
-
Absorbing Many-Body Correlations into Core-Optimized Orbitals
COO co-optimizes orbitals with TrimCI to absorb many-body correlations into the basis, cutting determinant count by orders of magnitude for iron-sulfur clusters versus localized bases or DMRG.
-
Long-range nonstabilizerness of topologically encoded states from mutual information
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
-
Combining non-parametric quantum states and MERA tensor networks for ground-state optimization
A hybrid method uses fixed quantum annealing states as boundary resources for classical MERA tensor networks to improve ground-state approximations without deeper quantum circuits.
-
Efficient Hamiltonian Engineering for Adiabatic MIS Algorithms
Engineered local Hamiltonian controls in Rydberg arrays accelerate adiabatic convergence to MIS solutions, raise success probabilities over global controls, and cut fidelity decay rate by 25% as graphs harden.
-
Quantum simulation of nanographenes and Trotter error cancellation
Trotter error cancellation in nanographene simulations reduces circuit depth by about 10x for quantum phase estimation of energy gaps to chemical accuracy in the Pariser-Parr-Pople model.
-
Emulation of large-scale qubit registers with a phase-space approach
A mean-field phase-space method emulates continuous-time dynamics of up to thousands of qubits with quadratic cost, capturing single-qubit observables qualitatively on transverse-field Ising models.
-
Single-layer framework of variational tensor network states
A single-layer variational tensor network method reduces computational cost by three orders of magnitude in bond dimension for 2D quantum models and confirms an intermediate empty-plaquette valence bond solid phase in the Shastry-Sutherland model.
-
Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
NN-fTNS enhance fermionic tensor networks with neural parametrization to improve expressivity and achieve order-of-magnitude better energies than pure fTNS on Hubbard models while maintaining linear scaling.
-
Neural and Tensor Networks in the Study of Quantum Annealing Processors
The thesis introduces a topology-aware tensor-network heuristic called SpinGlassPEPS.jl and thermodynamic metrics to benchmark quantum annealers on Ising problems while accounting for dissipation and effective temperature.
-
Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
-
Accelerating two-dimensional tensor network contractions using QR decompositions
A QR-based CTMRG variant accelerates iPEPS contractions by up to two orders of magnitude on GPUs with no accuracy loss for the Heisenberg and J1-J2 models.
-
Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
In a star network of qubits with XYZ Heisenberg interactions, localizable bipartite peripheral entanglement grows logarithmically with periphery size at zero xy-anisotropy and survives noisy measurements in the large-periphery limit.
-
Magnetic phases in the $J_{1}$-$J_{2}$ antiferromagnetic XY model on the honeycomb lattice
Numerical tensor-network study identifies Néel, Ising, collinear, and incommensurate spiral phases plus their transitions in the J1-J2 XY antiferromagnet on the honeycomb lattice.
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Exploring the performance of superposition of product states: from 1D to 3D quantum spin systems
The superposition of product states ansatz achieves high accuracy for ground state search in 1D and 3D tilted Ising models with short- and long-range interactions as well as random networks.
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Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems
Numerical examples show that the tensor network loop cluster expansion yields approximately exponential convergence of contraction error with cluster size for ground-state observables in high-bond-dimension tensor networks across 2D/3D spin and fermion systems.
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TensorNetwork on TensorFlow: Entanglement Renormalization for quantum critical lattice models
TensorFlow-backed TensorNetwork implementation of MERA for critical 1D Ising model with conformal data extraction and 200x GPU acceleration reported.
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Tensor Cookbook: Mastering Tensors through Diagrams
A guide presenting tensor algebra operations, decompositions, and gradients through tensor network diagrams for broader accessibility beyond quantum physics.
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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology
A review of how quantum information science is expected to provide new tools and insights for nuclear and high-energy physics phenomenology and quantum simulations.
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Pushing Tensor Networks to the Limit
Perspective article on continuous matrix product states (cMPS) proposed to overcome limitations in generalizing tensor networks to higher-dimensional continuum systems.
- Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series
- PEPSKit.jl: A Julia package for projected entangled-pair state simulations
- Grassmann corner transfer-matrix renormalization group approach to one-dimensional fermionic models
- Diagonal Isometric Form for Tensor Network States in Two Dimensions