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Fast-forwardability of qubit-mapped fermion models based on Cartan decomposition

Yuichiro Hidaka1,*, Shoichiro Tsutsui1, Shota Kanasugi2, Norifumi Matsumoto2, Kazunori Maruyama2, and Hirotaka Oshima2

  • 1QunaSys Inc., Aqua Hakusan Building 9F, 1-13-7 Hakusan, Bunkyo, Tokyo 113-0001, Japan
  • 2Quantum Laboratory, Fujitsu Research, Fujitsu Limited, 4-1-1 Kamikodanaka, Nakahara, Kawasaki, Kanagawa 211-8588, Japan

  • *Contact author: hidaka@qunasys.com
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Phys. Rev. Research 8, 033251 – Published 1 September, 2026

DOI: https://doi.org/10.1103/zzry-8h81

Abstract

We study the Hamiltonian algebra of qubit-mapped interacting fermion models and their fast-forwardability. We prove that the dimension of the Hamiltonian algebra of the fermion model with single-site Coulomb interaction is bounded from below by the exponential function of the number of sites, and the circuit depth of the Cartan-based fast-forwarding method for such a model also exhibits the same scaling. We apply this proposition to the Anderson impurity model and the Hubbard model and show that the dimension of the Hamiltonian algebra of these models scales exponentially with the number of sites. These behaviors of the Hamiltonian algebras imply that, under fermion-qubit mappings that map Majorana operators to single-term Pauli strings, the qubit models obtained from these fermion models cannot be efficiently simulated using the Cartan-based fast-forwarding method.

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Phys. Rev. Research 8, 033251– Published 1 September, 2026
  • Received 6 July 2025
  • Accepted 25 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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