Qubit-Regularized SU(2) and SU(3) Gauge Theories in Various Dimensions

We investigate qubit-regularized formulations of SU(2) and SU(3) gauge theories in d=2 and d=3 spatial dimensions using the monomer–dimer–tensor-network basis of the physical Hilbert space. This framework enables the construction of non-Abelian lattice gauge theories with finite-dimensional local Hilbert spaces that are free of sign problems, making them amenable to Quantum Monte Carlo (QMC) studies. In simple plaquette-chain geometries, parts of the phase structure can even be analyzed analytically. Building on recent results, we show that these models exhibit confinement–deconfinement transitions and critical behavior consistent with the universality classes expected from conventional lattice formulations, with some cases allowing systematic approaches toward the continuum limit. The qubit-regularized representation naturally provides a pathway toward simulating more realistic gauge theories on finite quantum systems.