A preprint posted to arXiv — not yet peer-reviewed — proposes a generalization of the sample-based Krylov quantum diagonalization (SKQD) method to compute single-particle Green's functions, a quantity central to many-body physics that encodes spectral and response properties of interacting systems. The key extension involves constructing Krylov subspaces in both the N+1 and N−1 particle-number sectors, sampling them on a quantum device, and then reconstructing the Green's function classically via a Lanczos continued-fraction expansion. The approach preserves SKQD's defining advantages: shallow circuits and no ancilla qubits, making it nominally compatible with near-term quantum hardware.
The authors demonstrate the method on the single-impurity Anderson model in a chain geometry, the standard setup used when embedding a correlated site into dynamical mean-field theory (DMFT). Across interaction strengths spanning the metal-insulator transition, they report that the main spectral features — including the Kondo resonance and Hubbard sidebands — are reproduced using only a small fraction of the full Hilbert space. The claim is that SKQD-based solvers could, in principle, handle DMFT bath representations with more sites than current quantum impurity solvers can manage practically.
These are promising indications, but several caveats apply. The results are numerical demonstrations rather than experimental quantum hardware runs, and the paper has not yet undergone peer review. How circuit depth, sampling overhead, and classical post-processing costs scale with bath size — and how the method performs under realistic noise — remain open questions that subsequent scrutiny will need to address.