Tensor network

[2][3] Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties.

It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network.

[10] In 1992, Steven R. White developed the Density Matrix Renormalization Group (DMRG) for quantum lattice systems.

[12] In 2002, Guifre Vidal and Reinhard Werner attempted to quantify entanglement, laying the groundwork for quantum resource theories.

In 2010, Ulrich Schollwock developed the density-matrix renormalization group for the simulation of one-dimensional strongly correlated quantum lattice systems.

In June 2019, Google, the Perimeter Institute for Theoretical Physics, and X (company), released TensorNetwork,[21] an open-source library for efficient tensor calculations.

Two tensor networks
Two different tensor network representations of a single 7-indexed tensor (both networks can be contracted to it with 7 free indices remaining). The bottom one can be derived from the top one by performing contraction on the three 3-indexed tensors (in yellow) and merging them together.
Tensor train technique