  Quantum algorithms for molecular electronic structure have been developed
with lower computational scaling than their classical counterparts, but
emerging quantum hardware is far from being capable of the
coherence,connectivity and gate errors required for their experimental
realization. Here we propose a class of quantum-classical hybrid algorithms
that compute the energy from a two-electron reduced density matrix (2-RDM). The
2-RDM is constrained by $N$-representability conditions, conditions for
representing an $N$-electron wavefunction, that mitigates noise from the
quantum circuit. We compute the strongly correlated dissociation of doublet
H$_{3}$ into three hydrogen atoms. The hybrid quantum-classical computer
matches the energies from full configuration interaction to 0.1 kcal/mol,
one-tenth of "chemical accuracy," even in the strongly correlated limit of
dissociation. Furthermore, the spatial locality of the computed one-electron
RDM reveals that the quantum computer accurately predicts the Mott
metal-insulator transition.
