{
  "abstract": "A quantum impurity model describes a small interacting subsystem embedded into a large bath of free fermions. Here we study the computational complexity of calculating the ground energy, thermal equilibrium, and dynamical properties of these models. Our work reveals a sharp contrast: equilibrium properties can be efficiently approximated by classical means, whereas time evolution can implement a universal quantum computation. More precisely, let $H$ be the Hamiltonian of an impurity model with $n$ fermionic modes and a constant-size impurity. We show that: (1) the ground energy of $H$ can be approximated to additive error $\\varepsilon$ by a classical algorithm with runtime $\\textsf{poly}(n,1/\\varepsilon)$, improving on the quasi-polynomial runtime of the best previously known algorithm; (2) at inverse temperature $β$, the Helmholtz free energy and a classical description of the thermofield double state can be computed to precision $\\varepsilon$ in time $\\textsf{poly}(n,β,1/\\varepsilon)$; (3) simulating the time evolution $e^{-iHt}$ is $\\textsf{BQP}$-complete, for $H$ that is time-independent and has a fixed, constant impurity size. Our algorithms exploit exponential suppression of multi-particle bath excitations in a basis organized by energy scale and Krylov depth. Our universality construction realizes a stationary quantum processor whose program arrives in a stream of freely propagating fermions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02130",
  "author_total": 6,
  "authors": [
    {
      "name": "Srinivasan Arunachalam"
    },
    {
      "name": "Sergey Bravyi"
    },
    {
      "name": "Anirban Chowdhury"
    },
    {
      "name": "Arkopal Dutt"
    },
    {
      "name": "Alexandru Gheorghiu"
    },
    {
      "name": "Zhi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fx6fh93cmwp7n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02130",
  "fulltext_url": null,
  "id": "fx6fh93cmwp7n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02130",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7216006615",
  "pdf_url": "https://arxiv.org/pdf/2610.02130",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fx6fh93cmwp7n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02130",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02130"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum impurity models: easy at equilibrium, universal in motion",
  "title_text": "Quantum impurity models: easy at equilibrium, universal in motion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/fx6fh93cmwp7n",
  "venue": "arXiv",
  "versions": []
}