Resolving correlated states of benzyne with an error-mitigated contracted quantum eigensolver

The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers [presented in Smart and Mazziotti, Phys. Rev. Lett. 126, 070504 (2021)10.1103/PhysRevLett.126.070504] in which a contraction of the Schrödinger equation is solved for the two-electron reduced density matrix (2-RDM) to resolve the energy splittings of the ortho-, meta-, and para-isomers of benzyne C6H4. In contrast to the traditional variational quantum eigensolver, the contracted quantum eigensolver can solve an integration (or contraction) of the many-electron Schrödinger equation onto the two-electron space. The quantum solution of the anti-Hermitian part of the contracted Schrödinger equation provides a scalable approach with few variational parameters that has its foundations in 2-RDM theory. Experimentally, a variety of error-mitigation strategies enable the calculation, including a linear shift in the 2-RDM targeting the iterative nature of the algorithm as well as a projection of the 2-RDM onto the convex set of approximately N-representable 2-RDMs defined by the 2-positive N-representability conditions. The relative energies exhibit single-digit millihartree errors, capturing a large part of the electron correlation energy, and the computed natural orbital occupations reflect the significant differences in the electron correlation of the isomers.