Determination of molecular excited states via symmetry guided subspace search variational quantum eigensolver

Quantitative simulations of photochemical reactions rely on highly accurate ab initio computations of the ground and excited electronic states. While substantial progress has been made in designing physically informed quantum algorithms to address the ground state under the constraints of near-term quantum hardware, relatively fewer developments exist for reliably computing excited state energetics, presumably due to the growing complexity of the quantum circuits for excited eigenroots. In this work, we exploit the inherent point-group and spin symmetries of molecular systems to construct symmetry-adapted sets of orthogonal reference states which are evolved with a common symmetry-scalar unitary, enabling the simultaneous determination of ground and excited eigenroots. By minimizing the energy functional over a restricted symmetry-adapted correlated manifold, the weighted subspace-search variational quantum eigensolver enables us to directly target multiple eigenroots within each spatial and spin symmetry sector. This physically motivated selection of references and the unitary confer substantial flexibility to the weighted energy landscape, largely allowing the optimization to avoid numerical traps and converge directly to the targeted eigenstates. More crucially, symmetry resolution also enables access to a larger number of eigenstates without substantially increasing the complexity of the cost function. Through benchmarking on moderate to strongly correlated molecular systems, we demonstrate the accuracy and advantages of our approach relative to several established excited state algorithms on quantum computers.