  Solving the electronic structure problem via unitary evolution of the
electronic Hamiltonian is one of the promising applications of digital quantum
computers. One of the practical strategies to implement the unitary evolution
is via Trotterization, where a sequence of short-time evolutions of
fast-forwardable (i.e. efficiently diagonalizable) Hamiltonian fragments is
used. Given multiple choices of possible Hamiltonian decompositions to
fast-forwardable fragments, the accuracy of the Hamiltonian evolution depends
on the choice of the fragments. We assess efficiency of multiple Hamiltonian
partitioning techniques using fermionic and qubit algebras for the
Trotterization. Use of symmetries of the electronic Hamiltonian and its
fragments significantly reduces the Trotter error. This reduction makes
fermionic-based partitioning Trotter errors lower compared to those in
qubit-based techniques. However, from the simulation-cost standpoint, fermionic
methods tend to introduce quantum circuits with a greater number of T-gates at
each Trotter step and thus are more computationally expensive compared to their
qubit counterparts.
