A QTN built by [1], called VQTN, uses an arbitrary two-qubit unitary gate parameterization based on the connectivity and gate set design of the trapped ions computers. This is inspired by the DDQCL model [2] that uses alternating layers of single qubit rotation gates and a Global Molmer-Sorensen gate (GMS) (a sequence of XX coupling/Ising gates).

References:

[1] R. Huang, X. Tan, and Q. Xu, “Variational quantum tensor networks classifiers,” Neurocomputing, vol. 452, pp. 89–98, Sep. 2021, doi: https://doi.org/10.1016/j.neucom.2021.04.074.
[2] M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, “A generative modeling approach for benchmarking and training shallow quantum circuits,” npj Quantum Information, vol. 5, no. 1, May 2019, doi: https://doi.org/10.1038/s41534-019-0157-8.

This gate parameterization can be, therefore, used to build other TNs and QCNN structures, and hence, should be added to the pipeline.