Claim record · edition 0.1.0
PEPS extend tensor networks beyond one dimension, but exact contraction of PEPS is computationally hard.
The lattice generalization of MPS gives the right entanglement structure for two-dimensional systems, and hardness results for contracting it are why higher-dimensional work uses approximate contraction schemes.
Limits of this claim
Approximate schemes carry errors that are not generally certified, so a two-dimensional tensor-network result requires more care in interpretation than a one-dimensional one.
Supporting sources
primary paper · identifier verified
Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
F. Verstraete, J. I. Cirac · 2004
arXiv:cond-mat/0407066
Primary source for the projected entangled pair state (PEPS) generalization of MPS beyond one dimension.
Source record →primary paper · identifier verified
The computational complexity of PEPS
Norbert Schuch, Michael M. Wolf, Frank Verstraete, J. Ignacio Cirac · 2006
arXiv:quant-ph/0611050
Establishes hardness results for contracting PEPS — the reason higher-dimensional tensor networks are approximated, not contracted exactly.
Source record →