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
40 Pith papers cite this work. Polarity classification is still indexing.
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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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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.
Tensor networks enable tunable, objective compression of 1D fluid data with lossless reconstruction at high bond dimension and efficient in-compressed-space operations like periodic convolution.
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.
Constructs explicit physical local operators whose expectation values match twist field actions in MPS, exact in the injectivity limit and at the center of orthogonality, with numerical tests in the transverse-field Ising model.
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.
A compact neural statebank based on autoregressive Transformers simulates 34-qubit quantum circuits with ~0.01 infidelity using 0.3 million parameters, outperforming tested approximate simulators.
Canonical mapping of quantum-dot-superconductor clusters enables neural quantum-state calculations that reveal trivial singlet, Heisenberg-like, and critical regimes with 1D gaplessness and 2D triplet states.
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.
Infinite PEPS simulations find a direct Néel-to-QSL transition at J2/J1 ≈ 0.08 in the triangular J1-J2 model and indicate the QSL is gapless, consistent with a U(1) Dirac spin liquid.
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