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

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.