Great fun to collaborate with @AnselmettiGian, Christian Gogolin and @QCWare's Rob Parrish on QNP gates and VQE ansätze from those for fermionic systems!
https://arxiv.org/abs/2104.05695 
There is quite a list of nice features of these gates and fabrics, including the following.

The gates preserve essential quantum numbers of the fermionic system, allowing us to construct a circuit within one specific symmetry sector, and at the same time are local, in the sense of acting on constant-size subsets of qubits and of locality in linear connectivity.

The ansätze we construct from those gates are expressive enough to reach the entire chosen symmetry sector of Hilbert space for deep circuits, but more importantly they yield good approximate solutions to the sought-after ground state at low depth and small parameter count.

It appears these gate fabrics are well-trainable, i.e. don't have the problem of vanishing gradients when increasing the parameter count /depth and initializing the parameters to simple constant values.

The fabrics keep it simple. They are constructed from a single constant-size gate block, which in turn has a simple expression in terms of orbital rotation and pair exchange. We also provide decompositions into elementary gates.

The major gates, i.e. Orbital rotations and pair exchange gate, satisfy a four-term parameter shift rule to compute the Gradient w.r.t. their parameter(s). We derive this rule and show it has the same measurement cost as the two-term rule.

While being nice for our QNP gates, this rule holds for all unitary gates with three distinct eigenvalue-generators (e.g. CRy). We exclude a type of further generalization and compare to the rule by @JakobKottmann, @theanandabhinav and @A_Aspuru_Guzik ( https://pubs.rsc.org/en/content/articlelanding/2021/SC/D0SC06627C#!divAbstract).