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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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 network simulations act as effective surrogate models for training QAOA on large 2D lattices, overcoming limits of parameter transfer from small instances and remaining classically feasible with moderate bond dimensions.
Tensor networks with belief propagation fail to simulate Google's quantum echoes OTOC experiment because the circuits produce largely incompressible entanglement.
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.
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.
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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.
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Tensor network surrogate models for variational quantum computation
Tensor network simulations act as effective surrogate models for training QAOA on large 2D lattices, overcoming limits of parameter transfer from small instances and remaining classically feasible with moderate bond dimensions.
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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.
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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.