Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory

• URL: http://arxiv.org/abs/2609.09147v1
• Date: Tue, 08 Sep 2026 17:59:00 GMT
• Title: Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory
• Abstract summary: We generalize the sample-based Krylov quantum diagonalization (SKQD) method from ground-state calculations to the evaluation of single-particle Green's functions.<n>Applying to the particle-hole-symmetric single-impurity Anderson model in chain geometry, the method recovers the spectral function using a relatively small fraction of the full Hilbert space.
• Score: 1.6871774025669009
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We generalize the sample-based Krylov quantum diagonalization (SKQD) method from ground-state calculations to the evaluation of single-particle Green's functions. By constructing and sampling unitary Krylov subspaces in the N +/- 1 particle-number sectors and evaluating all sector-connecting overlaps classically, the approach reconstructs the Green's function via a Lanczos continued fraction while retaining the shallow-circuit, ancilla-free character of SKQD. The quantum device is required only to prepare and sample short-time evolutions. Applied to the particle-hole-symmetric single-impurity Anderson model in chain geometry, with the discrete bath representation used in dynamical mean-field theory (DMFT), the method recovers the spectral function using a relatively small fraction of the full Hilbert space. Across a range of interaction strengths that spans the metal-insulator transition, the main spectral features are reproduced. These results suggest that SKQD-based Green's-function calculations may allow DMFT impurity solvers with a larger number of bath sites on near-term quantum hardware than is currently practical.

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