Fig. 9: Tensor network schematics for the orbital rotation heurisitics.

a A schematic of the FSWAP insertion. The vertical arrow denotes the combined operations of contraction into the two-site tensor followed by SVD in tensor network diagrammatic notation3,4. The horizontal arrow indicates merging into \({\hat{G}}_{ij}\) if the update is accepted. b A schematic of the steps to compute the truncation error cost function ξ(θ) in Eq. (21) for the classical univariate optimization to determine θopt. The adjoint rotation with angle − θopt is then merged into \({\hat{G}}_{ij}\).