In Trotterization, the typical Hamiltonian considered is:
$$ H = \sum_{p, q} h_{pq} a^{\dagger}_p a_q + \sum_{p, q, r, s} a^{\dagger}_p a^{\dagger}_q a_r a_s $$
Which is then converted into a sequence of gates by the Jordan Wigner transformation.
However, how do we choose the ordering of the $ pq$ and $pqrs$ terms? For example, if our Hamiltonian was:
$$ H = (a^{\dagger}_1 a_2 + a^{\dagger}_2 a_1) + (a^{\dagger}_2 a_3 + a^{\dagger}_3 a_2) + (a^{\dagger}_1 a^{\dagger}_2 a_2 a_3 + a^{\dagger}_3 a^{\dagger}_2 a_2 a_1)$$
There are at least $ 3! = 6$ ways to order the Hamiltonian, a number which quickly explodes as the size of the Hamiltonian grows.
Note that the terms don't have clean commutation rules - sometimes the terms will commute or anticommute. Is there an approach to ordering the Hamiltonian that maximizes simulation accuracy?