Implementation of Measurement Reduction for the Variational Quantum Eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of state preparation and measurement steps required to estimate different terms in the Hamiltonian of interest. Here we investigate two different implementations of the unitary partitioning measurement reduction strategy achieved by (1) a sequence of rotations and (2) a linear combination of unitaries (LCU). Simulations show this reduction can significantly benefit calculations by reducing the standard error of the mean. To our knowledge, this work also demonstrates the first experimental execution of LCU on quantum hardware.