Inspired from the ideas from this paper, I'd like to provide an automated structural optimisation algorithm to the TTN simulator.
I believe this should be done regularly when applying a two-qubit gate if the bond dimension is deemed to be large enough that it's worth to try it.
I believe this should restrict to keeping the tree balanced and just swapping qubits between leaves.
I believe this swapping should be informed by the entropy (or Schmidt rank) between each pair of (qubit, leaf-node). This metric can be efficiently calculated from the TTN via qubit discarding.
Inspired from the ideas from this paper, I'd like to provide an automated structural optimisation algorithm to the TTN simulator.