Evaluating the efficiency of ground state preparation algorithms*

In recent years, a lot of effort has been devoted to the development of different ground-state energy estimation (GSEE) algorithms for molecules and materials. To make GSEE methods practical, it is important to reduce their runtime which highly depends on the features of ground-state preparation (GSP) methods. Specifically, the magnitude of the ansatz overlap plays a crucial role in the performance of GSEE algorithms and the realization of a potential quantum advantage. In this work, we asked under which conditions a GSP method is acceptable over a reference method, such as the Hartree-Fock. We introduce the criteria under which a GSP method is acceptable for the purposes of ground state energy estimation. We consider different GSP methods ranging from heuristics to algorithms with provable performance guarantees. We perform numerical simulations to benchmark their performance on different problems and discuss the notion of “good” overlap. A GSP method needs to provide a better trade-off between the resource cost and the overlap provided to be accepted over the reference method. This work sets the ground to further explore the requirements to achieve quantum advantage in quantum chemistry.