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The rapid progress in quantum computing has opened up new possibilities fortackling complex scientific problems. Variational quantum eigensolver (VQE)holds the potential to solve quantum chemistry problems and achieve quantumadvantages. However, the measurement step within the VQE framework presentschallenges. It can introduce noise and errors while estimating the objectivefunction with a limited measurement budget. Such error can slow down or preventthe convergence of VQE. To reduce measurement error, many repeated measurementsare needed to average out the noise in the objective function. By consolidatingHamiltonian terms into cliques, simultaneous measurements can be performed,reducing the overall measurement shot count. However, limited prior knowledgeof each clique, such as noise level of measurement, poses a challenge. Thiswork introduces two shot assignment strategies based on estimating the standarddeviation of measurements to improve the convergence of VQE and reduce therequired number of shots. These strategies specifically target two distinctscenarios: overallocated and underallocated shots. The efficacy of theoptimized shot assignment strategy is demonstrated through numericalexperiments conducted on a H$_2$ molecule. This research contributes to theadvancement of VQE as a practical tool for solving quantum chemistry problems,paving the way for future applications in complex scientific simulations onquantum computers.

Optimizing Shot Assignment in Variational Quantum Eigensolver Measurement