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.
Belief Propagation and Tensor Network Expansions for Many-Body Quantum Systems: Rigorous Results and Fundamental Limits
7 Pith papers cite this work. Polarity classification is still indexing.
7
Pith papers citing it
abstract
Belief propagation (BP) provides a scalable heuristic for contracting tensor networks on loopy graphs, but its success in quantum many-body settings has largely rested on empirical evidence. Developing upon a recently introduced cluster-expansion framework for tensor networks, we rigorously study the applicability of BP to many-body quantum systems. For a state represented as a PEPS satisfying a ``loop-decay" condition, we prove that BP supplemented by cluster corrections approximates local observables with exponentially small relative error, and we give explicit formulas expressing local expectation values as BP predictions dressed by connected clusters intersecting the observable region. This representation establishes a direct link between cluster corrections and physical correlation functions. As a result, we show that ``loop-decay" \emph{necessarily implies} exponential decay of connected correlations, yielding sharp, rigorous criteria for when BP can and cannot succeed, and ruling out its validity at critical points. Numerical simulations of the two- and three-dimensional transverse field Ising model at zero and finite temperature confirm our analytical predictions, demonstrating quantitative accuracy deep in gapped phases and systematic failure near criticality.
citation-role summary
background 1
citation-polarity summary
years
2026 7roles
background 1polarities
background 1representative citing papers
Tensor-network simulation of the ruby-lattice antiferromagnet finds magnetic plateaus hosting simplex liquid states with residual entropy and continuous heat capacity at low but finite temperature.
Presents IRD-GrAPE optimal control to generate GHZ, Dicke, and extremal states in dipolar Rydberg arrays by truncating the Hilbert space to capture leakage with linear scaling.
All-step fixed-point amplitude amplification on IBM Heron preserves sequential Tiger POMDP posteriors and planner actions across 8–32 step horizons inside a measured operating envelope.
Numerical iPEPS with loop expansions indicates the SU(4) Heisenberg model on the hyperhoneycomb lattice has a gapless quantum spin-liquid ground state, consistent with prior variational Monte Carlo results.
Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
citing papers explorer
-
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.
-
Finite-temperature formation of magnetic plateaus and simplex liquid states on the frustrated ruby lattice
Tensor-network simulation of the ruby-lattice antiferromagnet finds magnetic plateaus hosting simplex liquid states with residual entropy and continuous heat capacity at low but finite temperature.
-
Quantum optimal control of the Dicke manifold in dipolar Rydberg atom arrays
Presents IRD-GrAPE optimal control to generate GHZ, Dicke, and extremal states in dipolar Rydberg arrays by truncating the Hilbert space to capture leakage with linear scaling.
-
QANTIS: Hardware-Calibrated Sequential POMDP Belief Updates on IBM Heron
All-step fixed-point amplitude amplification on IBM Heron preserves sequential Tiger POMDP posteriors and planner actions across 8–32 step horizons inside a measured operating envelope.
-
SU(4) Heisenberg model on the hyperhoneycomb lattice
Numerical iPEPS with loop expansions indicates the SU(4) Heisenberg model on the hyperhoneycomb lattice has a gapless quantum spin-liquid ground state, consistent with prior variational Monte Carlo results.
-
Contracting Tensor Networks with Generalized Belief Propagation
Generalized belief propagation approximates tensor network contractions via hierarchical region messages and fixed-point solutions, demonstrated on Ising, ice, AKLT, and random tensor networks.
-
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.