{
  "id": "2501.17863",
  "version": "v1",
  "published": "2025-01-29T18:59:59.000Z",
  "updated": "2025-01-29T18:59:59.000Z",
  "title": "Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to $\\mathbb{D}_8$",
  "authors": [
    "Emanuele Gaz",
    "Pavel P. Popov",
    "Guy Pardo",
    "Maciej Lewenstein",
    "Philipp Hauke",
    "Erez Zohar"
  ],
  "categories": [
    "hep-lat",
    "quant-ph"
  ],
  "abstract": "In this work, we address the problem of a resource-efficient formulation of non-Abelian LGTs by focusing on the difficulty of simulating fermionic degrees of freedom and the Hilbert space redundancy. First, we show a procedure that removes the matter and improves the efficiency of the hardware resources. We demonstrate it for the simplest non-Abelian group addressable with this procedure, $\\mathbb{D}_8$, both in the cases of one (1D) and two (2D) spatial dimensions. Then, with the objective of running a variational quantum simulation on real quantum hardware, we map the $\\mathbb{D}_8$ lattice gauge theory onto qudit systems with local interactions. We propose a variational scheme for the qudit system with a local Hamiltonian, which can be implemented on a universal qudit quantum device as the one developed in $\\href{https://doi.org/10.1038/s41567-022-01658-0}{[Nat. Phys. 18, 1053 (2022)]}$. Our results show the effectiveness of the matter-removing procedure, solving the redundancy problem and reducing the amount of quantum resources. This can serve as a way of simulating lattice gauge theories in high spatial dimensions, with non-Abelian gauge groups, and including dynamical fermions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-29T18:59:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lattice gauge theory",
      "non-abelian lattice gauge theories",
      "variational approach",
      "universal qudit quantum device",
      "qudit system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}