Concept record · edition 0.1.0
PEPS
A projected entangled pair state: the generalization of MPS to two and higher dimensions, with tensors arranged on a lattice.
Why it matters
It extends the tensor-network approach past the chain geometry where MPS applies.
What this does not establish
Exact contraction of PEPS is computationally hard, so higher-dimensional work relies on approximate contraction schemes whose error is not generally certified.
Claims using this concept
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 →