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

Abstract

We study methods for efficient preparation of approximate ground states of $SU(3)$ 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 $2\times 2$ 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 \texttt{ymcirc} -- a package of tools for building $SU(3)$ circuits and processing measurements -- and \texttt{pyclebsch}, a package for efficiently computing $SU(N)$ Clebsch-Gordan coefficients.

Comments: 40 pages. v3: typos fixed, version published in PRD. v2: updated refs. The SU(3) circuit-generating package ymcirc is available from https://github.com/hepqis-uiuc/ymcirc and the SU(N) Clebsch-Gordan package is available from https://github.com/hepqis-uiuc/pyclebsch . A Jupyter notebook demonstrating a ymcirc workflow is included in the ancillary files