Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes

L. Spagnoli; A. Roggero; N. Wiebe

doi:10.22331/q-2026-01-16-1968

Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes

L. Spagnoli^1,2, A. Roggero^1,2, and N. Wiebe^3,4,5

¹Dipartimento di Fisica, University of Trento, via Sommarive 14, I–38123, Povo, Trento, Italy
²INFN-TIFPA Trento Institute of Fundamental Physics and Applications, Trento, Italy
³Department of Computer Science, University of Toronto, Toronto, ON M5S 2E4, Canada
⁴Pacific Northwest National Laboratory, Richland, WA 99354, USA
⁵Department of Physics, University of Washington, Seattle, WA 98195, USA

Published:	2026-01-16, volume 10, page 1968
Editor:	Alioscia Hamma
Eprint:	arXiv:2405.19293v3
Doi:	https://doi.org/10.22331/q-2026-01-16-1968
Citation:	Quantum 10, 1968 (2026).

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Abstract

We show in this paper that a strong and easy connection exists between quantum error correction and Lattice Gauge Theories (LGT) by using the Gauge symmetry to construct an efficient error-correcting code for Abelian $\mathbb{Z_2}$ LGTs. We identify the logical operations on this gauge covariant code and show that the corresponding Hamiltonian can be expressed in terms of these logical operations while preserving the locality of the interactions. Furthermore, we demonstrate that these substitutions actually give a new way of writing the LGT as an equivalent hardcore boson model. Finally we demonstrate a method to perform fault-tolerant time evolution of the Hamiltonian within the gauge covariant code using both product formulas and qubitization approaches. This opens up the possibility of inexpensive end to end dynamical simulations that save physical qubits by blurring the lines between simulation algorithms and quantum error correcting codes.

► BibTeX data

@article{Spagnoli2026faulttolerant,
  doi = {10.22331/q-2026-01-16-1968},
  url = {https://doi.org/10.22331/q-2026-01-16-1968},
  title = {Fault-tolerant simulation of {L}attice {G}auge {T}heories with gauge covariant codes},
  author = {Spagnoli, L. and Roggero, A. and Wiebe, N.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {1968},
  month = jan,
  year = {2026}
}

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