Diagonalizing large many-body systems on a quantum processor using Krylov quantum method

Estimating low-energy states in many-body systems is fundamental in computational quantum science. While variational quantum algorithms offer a way to prepare ground states on early quantum processors, their unreliable convergence and excessive demands on cost function evaluations hinder their application to larger systems. Thus, alternative approaches are essential for scaling experiments on pre-fault-tolerant quantum devices. In this study, we leverage a superconducting quantum processor to calculate eigenenergies of quantum many-body systems on 2D lattices with up to 56 sites, employing the Krylov quantum diagonalization method—a quantum analog of classical diagonalization techniques. By constructing subspaces of the many-body Hilbert space through Trotterized unitary evolutions on the quantum processor, we can then perform classical diagonalization of the interacting Hamiltonians within these subspaces. Our results indicate that quantum diagonalization algorithms are well-poised to complement classical techniques, reinforcing the computational approaches foundational to quantum systems analysis.