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.
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.
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.
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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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.
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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.