Ground and Excited States from Quantum Manifold Approaches

Variational approaches for quantum computing offer flexible ways to prepare and improve quantum states relevant for chemistry and physics, though the optimization problem is limited by the structure of the variational ansatz. For excited states, orthogonality in the procedure often results in a constrained approach or a generalized eigenvalue problem. In this work, we look at solutions of the ground and excited state problem using manifold-based techniques, using structures which naturally encode constraints, and a framework that directly optimizes the state. In particular, we focus on the energy minimization problem and the invariant subspace minimization problem.