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The simulation of strongly correlated many-electron systems is one of themost promising applications for near-term quantum devices. Here we use a classof eigenvalue solvers (presented in Phys. Rev. Lett. 126, 070504 (2021)) inwhich a contraction of the Schr\"odinger equation is solved for thetwo-electron reduced density matrix (2-RDM) to resolve the energy splittings ofortho-, meta-, and para-isomers of benzyne ${\textrm C_6} {\textrm H_4}$. Incontrast to the traditional variational quantum eigensolver, the contractedquantum eigensolver solves an integration (or contraction) of the many-electronSchr\"odinger equation onto the two-electron space. The quantum solution of theanti-Hermitian part of the contracted Schr\"odinger equation (qACSE) provides ascalable approach with variational parameters that has its foundations in 2-RDMtheory. Experimentally, a variety of error mitigation strategies enable thecalculation, including a linear shift in the 2-RDM targeting the iterativenature of the algorithm as well as a projection of the 2-RDM onto the convexset of approximately $N$-representable 2-RDMs defined by the 2-positive (DQG)$N$-representability conditions. The relative energies exhibit single-digitmillihartree errors, capturing a large part of the electron correlation energy,and the computed natural orbital occupations reflect the significantdifferences in the electron correlation of the isomers.

Resolving Correlated States of Benzyne on a Quantum Computer with an Error-Mitigated Quantum Contracted Eigenvalue Solver