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  • Open Access

Quantum circuits for SU(3) lattice gauge theory

Praveen Balaji1, Cianán Conefrey-Shinozaki1, Patrick Draper1,*, Jason K. Elhaderi1, Drishti Gupta1, Luis Hidalgo1, Andrew Lytle1, and Enrico Rinaldi2

  • 1Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
  • 2Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan

  • *Contact author: pdraper@illinois.edu
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Phys. Rev. D 112, 054511 – Published 24 September, 2025

DOI: https://doi.org/10.1103/k8f6-yft8

Abstract

Lattice gauge theories in varying dimensions, lattice volumes, and truncations offer a rich family of targets for Hamiltonian simulation on quantum devices. In return, formulating quantum simulations can provide new ways of thinking about the quantum structure of gauge theories. In this work, we consider pure SU(3) gauge theory in two and three spatial dimensions in a streamlined version of the electric basis. We use a formulation of the theory that balances locality of the Hamiltonian and size of the gauge-invariant state space, and we classically pre-compute dictionaries of plaquette operator matrix elements for use in circuit construction. We build circuits for simulating time evolution on arbitrary lattice volumes, spanning circuits suitable for Noisy Intermediate-Scale Quantum era hardware to future fault-tolerant devices. Relative to spin models, time evolution in lattice gauge theories involves more complex local unitaries, and the Hilbert space of all quantum registers may have large unphysical subspaces. Based on these features, we develop general, volume-scalable tools for optimizing circuit depth, including pruning and fusion algorithms for collections of large multicontrolled unitaries. We describe scalings of quantum resources needed to simulate larger circuits and some directions for future algorithmic development.

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Physics Subject Headings (PhySH)

Corrections

7 November, 2025

Correction: Missing lines in the quantum circuits represented in Eq. (23), Eq. (25), Fig. 5, and Fig. 6 have been restored.

Article Text

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Outline

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Phys. Rev. D 112, 054511– Published 24 September, 2025
  • Received 11 May 2025
  • Accepted 26 August 2025
  • Corrected 7 November 2025
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