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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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.
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.
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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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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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Mind the gaps: The fraught road to quantum advantage
The paper identifies four key hurdles in the transition from NISQ to FASQ quantum computers and argues that targeting them will accelerate progress toward useful quantum advantage.