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arXiv:2509.25865 · Physical review. D/Physical review. D.

Perturbation theory, irrep truncations, and state preparation methods for quantum simulations of S U ( 3 ) lattice gauge theory

Praveen Balaji, Cianán Conefrey-Shinozaki, Patrick Draper, Jason K. Elhaderi, Drishti Gupta, Luis Hidalgo, Andrew Lytle

Published Apr 15, 2026• 1 citation
arXivHTMLPDF

Abstract

We study methods for efficient preparation of approximate ground states of S U ( 3 ) lattice gauge theory on quantum hardware. Working in a variant of the electric basis, we introduce a refinement of the irrep truncation based on the energy density of site singlets, which provides a finer gradation of simulation complexity. Using strong-coupling perturbation theory as a guide, we develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices, including the 2 × 2 plaquette lattice in d = 2 and the cube in d = 3 . We contrast state fidelities and resource requirements of variational methods against adiabatic state preparation and introduce a method that hybridizes the two approaches. Finally, we report on the public release of —a package of tools for building S U ( 3 ) circuits and processing measurements—and , a package for efficiently computing S U ( N ) Clebsch–Gordan coefficients.

DOI
10.1103/m719-7tdf

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We study methods for efficient preparation of approximate ground states of S U ( 3 ) lattice gauge theory on quantum hardware. Working in a variant of the electric basis, we introduce a refinement of the irrep truncation based on the energy density of site singlets, which provides a finer gradation of simulation complexity. Using strong-coupling perturbation theory as a guide, we develop simple ansatz circuits for ground state preparation and test them via classical simulation on small lattices, including the 2 × 2 plaquette lattice in d = 2 and the cube in d = 3 . We contrast state fidelities and resource requirements of variational methods against adiabatic state preparation and introduce a method that hybridizes the two approaches. Finally, we report on the public release of —a package of tools for building S U ( 3 ) circuits and processing measurements—and , a package for efficiently computing S U ( N ) Clebsch–Gordan coefficients.
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Gauge theories like lattice QCD present a complex problem for quantum simulation. In a basis where the electric part of the Hamiltonian is simple, the magnetic part, generally expressed as a sum over the plaquette operators of the lattice, is quite complicated, producing correlated transitions between several link and site degrees of freedom. We provide an efficient block encoding of the plaquette operator in the irrep basis, a refinement of the electric basis where the internal gauge-variant degrees of freedom are integrated out. The construction removes the plaquette matrix element scaling wall which has been a significant barrier for other approaches in this basis. The algorithm leverages a convenient factorization property of the matrix elements, cheap classical precomputation, and quantum oracles built from lookup tables and programmed rotations.