Exploring Variational Regularization of Krylov Subspaces

arXiv:2611.09229v1 Announce Type: new Abstract: Krylov subspace methods efficiently approximate extremal eigenstates and eigenvalues of many-body Hamiltonians, but non-orthogonal bases can suffer from ill-conditioning. This challenge is amplified in quantum computing, where direct state access and thus straightforward orthogonalization are unavailable. We investigate a variational Krylov-like framework that iteratively optimizes a parametrized sequence of states to mimic Lanczos-like couplings while penalizing linear dependencies.