  One limitation of the variational quantum eigensolver algorithm is the large
number of measurement steps required to estimate different terms in the
Hamiltonian of interest. Unitary partitioning reduces this overhead by
transforming the problem Hamiltonian into one containing fewer terms. We
explore two different circuit constructions of the transformation required -
one built by a sequence of rotations and the other a linear combination of
unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and
studied the ground states of H2 and LiH. Both implementations are successful
even in the presence of noise. The sequence of rotations realization offers the
greatest benefit to calculations, whereas the probabilistic nature of LCU
reduces its effectiveness. To our knowledge, this work also demonstrates the
first experimental implementation of LCU on quantum hardware.
