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

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

This arXiv preprint generalizes the sample-based Krylov quantum diagonalization (SKQD) method from ground-state energy calculations to computing single-particle Green's functions on quantum hardware. By building unitary Krylov subspaces in the N±1 particle sectors and classically evaluating overlaps, the authors reconstruct Green's functions via a Lanczos continued fraction, applying the technique as an impurity solver for dynamical mean-field theory (DMFT) on the single-impurity Anderson model, reproducing spectral features across the metal-insulator transition with shallow, ancilla-free quantum circuits.

TL;DR Extends sample-based Krylov quantum diagonalization to Green's-function/DMFT impurity solving on near-term quantum hardware.
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What it claims

The paper extends SKQD to compute single-particle Green's functions and uses it as a DMFT impurity solver. Beyond what the summary states, the abstract adds a concrete resource claim: the method recovers the spectral function using "a relatively small fraction of the full Hilbert space," and the stated payoff is enabling DMFT impurity solvers with more bath sites on near-term quantum hardware than is currently practical.

How it works

The setting is the particle-hole-symmetric single-impurity Anderson model in chain geometry, using the discrete bath representation standard in DMFT. Krylov subspaces are built and sampled in the N±1 particle-number sectors; all sector-connecting overlaps are evaluated classically, and the Green's function is reconstructed via a Lanczos continued fraction. The quantum device's only role is to prepare and sample short-time evolutions — no ancilla, shallow circuits — with the continued-fraction reconstruction done classically.

Evidence

Across a range of interaction strengths spanning the metal-insulator transition, the main spectral features are reproduced. The abstract gives no hardware run, qubit count, bath-site count, sampling budget, or error metric — the "small fraction of the full Hilbert space" is stated qualitatively, not quantified.

Limits

This is an abstract-only fetch; no figures, tables, or numbers are available. What is reported is stated as recovering "main spectral features," not full quantitative agreement, suggesting the reconstruction is approximate. The demonstration is confined to the particle-hole-symmetric single-impurity Anderson model in chain geometry — asymmetric fillings, multi-orbital impurities, and other bath geometries are untested. The larger-bath-site advantage is framed as a suggestion ("may allow"), not a demonstrated result; whether the experiments were run on real hardware or simulated is not stated in the abstract. An engineer weighing adoption should read the PDF for qubit counts, sampling overhead, and the actual bath size reached.

Organisations named here

  • Dynamical Mean-Field Theory
  • single-impurity Anderson model
  • SKQD

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