# 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

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

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