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Quantum algorithms for molecular electronic structure have been developedwith lower computational scaling than their classical counterparts, butemerging quantum hardware is far from being capable of thecoherence,connectivity and gate errors required for their experimentalrealization. Here we propose a class of quantum-classical hybrid algorithmsthat compute the energy from a two-electron reduced density matrix (2-RDM). The2-RDM is constrained by $N$-representability conditions, conditions forrepresenting an $N$-electron wavefunction, that mitigates noise from thequantum circuit. We compute the strongly correlated dissociation of doubletH$_{3}$ into three hydrogen atoms. The hybrid quantum-classical computermatches the energies from full configuration interaction to 0.1 kcal/mol,one-tenth of "chemical accuracy," even in the strongly correlated limit ofdissociation. Furthermore, the spatial locality of the computed one-electronRDM reveals that the quantum computer accurately predicts the Mottmetal-insulator transition.

Quantum-classical hybrid algorithm using an error-mitigating $N$-representability condition to compute the Mott metal-insulator transition