Automatic determination of tree tensor network structures

Here are some references:

1. Measuring orbital interaction using quantum information theory (https://arxiv.org/abs/cond-mat/0508524)
2. Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks (https://arxiv.org/abs/1006.3095)
3. Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm (https://arxiv.org/abs/1302.2298)
4. Tensor product methods and entanglement optimization for ab initio quantum chemistry (https://arxiv.org/abs/1412.5829)
5. Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems (https://pubs.acs.org/doi/10.1021/ct501187j)
6. Simulating quantum circuits using tree tensor networks (https://arxiv.org/abs/2206.01000)
7. Automatic structural optimization of tree tensor networks (https://arxiv.org/abs/2209.03196)
8. Entanglement bipartitioning and tree tensor networks (https://arxiv.org/abs/2210.11741)
9. Visualization of Entanglement Geometry by Structural Optimization of Tree Tensor Network (https://arxiv.org/abs/2401.16000)

@JoeyT1994

Start by reviewing the nine linked references and the package's existing tools for higher-dimensional tensor networks. Determine what automatic tree-structure selection should accept, produce, and optimize. Done means the intended structure-determination behavior is defined and implemented with validation against the relevant tensor-network cases.