The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory

Quantum simulations of QCD require digitization of the infinite-dimensional gluon field. Schemes for doing this with the minimum amount of qubits are desirable. We present a practical digitization for $SU(3)$ gauge theories via its discrete subgroup $S(1080)$. Using a modified action that allows classical simulations down to $a\approx 0.08$ fm, the low-lying glueball spectrum is computed with percent-level precision at multiple lattice spacings and shown to extrapolate to the continuum limit $SU(3)$ results. This suggests that this digitization scheme is sufficient for precision quantum simulations of QCD.