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This research extends sample-based Krylov quantum diagonalization to compute Green's functions, enabling near-term quantum hardware to tackle larger bath sites in dynamical mean-field theory simulations. By leveraging shallow circuits and classical post-processing of sector overlaps, the method effectively reconstructs spectral functions across metal-insulator transitions without requiring deep quantum resources. The approach represents a significant step toward practical quantum advantage for solving strongly correlated electron problems in materials science.
Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory
arXiv:2609.09147v1 Announce Type: cross 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.
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.
Strongly Correlated Electrons (cond-mat.str-el); Materials Science (cond-mat.mtrl-sci); Quantum Physics (quant-ph)
arXiv:2609.09147 [cond-mat.str-el]
(or arXiv:2609.09147v1 [cond-mat.str-el] for this version)
https://doi.org/10.48550/arXiv.2609.09147 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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