Implementation of measurement reduction for the variational quantum eigensolver

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 built by 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. This work also demonstrates an experimental implementation of LCU on quantum hardware.