Variational quantum eigensolvers (VQEs) constitute a class of hybrid quantum-classical simulation algorithms that are envisioned as possibly appropriate for noisy intermediate scale quantum processors. For VQEs to be useful, it is important to reduce the size of the ansatz and the number of required measurements. I will present our work addressing these issues with an adaptive, problem tailored approach to ansatz construction. I will also discuss recent work showing how the overhead can be lowered in ADAPT-VQE.
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