  The rapid progress in quantum computing has opened up new possibilities for
tackling complex scientific problems. Variational quantum eigensolver (VQE)
holds the potential to solve quantum chemistry problems and achieve quantum
advantages. However, the measurement step within the VQE framework presents
challenges. It can introduce noise and errors while estimating the objective
function with a limited measurement budget. Such error can slow down or prevent
the convergence of VQE. To reduce measurement error, many repeated measurements
are needed to average out the noise in the objective function. By consolidating
Hamiltonian terms into cliques, simultaneous measurements can be performed,
reducing the overall measurement shot count. However, limited prior knowledge
of each clique, such as noise level of measurement, poses a challenge. This
work introduces two shot assignment strategies based on estimating the standard
deviation of measurements to improve the convergence of VQE and reduce the
required number of shots. These strategies specifically target two distinct
scenarios: overallocated and underallocated shots. The efficacy of the
optimized shot assignment strategy is demonstrated through numerical
experiments conducted on a H$_2$ molecule. This research contributes to the
advancement of VQE as a practical tool for solving quantum chemistry problems,
paving the way for future applications in complex scientific simulations on
quantum computers.
