PEPS Tensor Network

The PEPS tensor network (projected entangled pair states)[1][2] generalizes the matrix product state / tensor train tensor network from a one-dimensional network to a network on an arbitrary graph.

The tensor diagram for a PEPS on a finite square lattice is:

Explanation of the Name PEPS

The name PEPS comes from a quantum information viewpoint that generic tensor networks can be viewed as maximally correlated (or entangled) tensors in multiple copies of the tensor index space which are then projected into a single copy of the index space.

In an more general mathematics context, a better name for these networks might be tensor grid or tensor lattice networks.

Applications of PEPS in Quantum Physics

PEPS tensor networks have primarily been used as an ansatz for quantum wavefunctions, more specifically ground states of two-dimensional Hamiltonians.

References

1. Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions, F. Verstraete, J. I. Cirac, arxiv:0407066 (2004)
2. Valence-bond states for quantum computation, F. Verstraete, J. I. Cirac, Phys. Rev. A 70, 060302 (2004), quant‑ph/0311130

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