Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory
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.
Related
- Sample-based Quantum Diagonalization via Density Matrix Renormalization Group
- A scalable sample-based quantum diagonalization solver for general Pauli-sum Hamiltonians
- Code-space recovery for sample-based quantum diagonalization beyond native symmetry constraints
- Sample-Based Quantum Diagonalization for Variable Molecular Geometries
- Extending Sample-based Quantum Diagonalization to Systems of Linear Equations
BibTeX
@misc{patel2026greens,
title = {{Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory}},
author = {Jay Patel and Chakradhar Rangi and Ka-Ming Tam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09147},
eprint = {2609.09147},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09147},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Green's Functions from Sample-based Krylov Quantum Diagonalization: An Impurity Solver for Dynamical Mean-Field Theory
AU - Jay Patel
AU - Chakradhar Rangi
AU - Ka-Ming Tam
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09147
UR - https://arxiv.org/abs/2609.09147
AB - 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.
ER -