Evaluating Sample-Based Krylov Quantum Diagonalization for Heisenberg Models with Applications to Materials Science

We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and magnetization sector sweeps, we investigate SKQD for problems with non-sparse ground states, where energy accuracy and sampling efficiency are theoretically anticipated to degrade. Our studies reveal that SKQD reproduces ground-state energies and field-dependent magnetization across a range of anisotropies. Benchmarks against DMRG and exact diagonalization show consistent qualitative agreement, with accuracy improving systematically in more anisotropic regimes. We further demonstrate SKQD on quantum hardware by implementing 18- and 30-qubit Heisenberg chains, obtaining magnetization curves that match theoretical expectations. Simulations on the IBM Nighthawk processor for 64-qubit two-dimensional square lattice systems further indicate that the method remains effective beyond one-dimensional geometries.