Determination of Molecular Symmetry Adapted Eigenroots in the Variational Quantum Eigensolver Framework

ABSTRACT Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in near‐term quantum devices. While the VQE is traditionally tailored to determine the ground state wavefunction with the underlying Rayleigh‐Ritz principle, for molecules characterized by a given point group symmetry, we propose to unify the VQE framework to treat the lowest energy states of any irreducible representation and spin‐multiplicity. The method relies on the construction of a symmetry adapted multi determinantal reference where the constituent determinants are entangled through appropriate Clebsch‐Gordan coefficients to ensure the desired spin‐multiplicity. The unitary operator, defined in terms of totally symmetric spin‐free generators, safeguards the method against variational collapse to symmetry broken solutions. We also propose an energy sorting based adaptive ansatz construction algorithm starting from a pool of totally symmetric spin‐free unitary generators to come up with dynamically optimal ansatz. The proposed methodology allows us to build up further search algorithms within a reduced dimensional symmetry‐adapted sub‐Hilbert‐space. With a highly compact circuit structure, it is expected to be realized in the near‐term quantum devices to study emerging chemical phenomena and exploration of novel chemical space.