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Quantum simulation of quantum chemistry is one of the most compelling applications of quantum computing. It is of particular importance in areas ranging from materials science, biochemistry, and condensed matter physics. Here, we propose a full quantum eigensolver (FQE) algorithm to calculate the molecular ground energies and electronic structures using quantum gradient descent. Compared to existing classical-quantum hybrid methods such as variational quantum eigensolver (VQE), our methoddoi:10.34133/2020/1486935 pmid:32274468 pmcid:PMC7125455 fatcat:vj3khb4agnfgpduqt3sdjlmy3e