Fig. 4: Graph representations of matrix product states.

a MPSs \(\left\vert {\phi }_{j}\right\rangle\) and \(\left\vert {\phi }_{i}\right\rangle\) with different site orderings over the same set of N = 6 molecular orbitals, and the superposition state \({c}_{i}\left\vert {\phi }_{i}\right\rangle +{c}_{j}\left\vert {\phi }_{j}\right\rangle\). b A sequence of FSWAP operations \({\hat{F}}_{ij}\) transforms the MPS \(\left\vert {\phi }_{i}\right\rangle\) into the orbital ordering of \(\left\vert {\phi }_{j}\right\rangle\), giving rise to the tensor network in Fig. 5a.