Symmetry-initialized quantum Gibbs sampling: a non-Abelian asymmetry cascade
This work addresses the mixing bottleneck faced by quantum Gibbs samplers under weak symmetry breaking by proposing an acceleration framework grounded in group representation theory. By constructing an asymmetry cascade mechanism within non-Abelian groups, the study reveals that matching only the first moment is insufficient to eliminate slow-mode overlap; instead, a projection operation based on group-averaged asymmetry is required. The approach integrates representation theory, group-invariant input construction, subgroup lattice indexing, and the Davies master equation model. When applied to an SU(2) Davies sampler, it achieves a relaxation rate that scales linearly with the symmetry-breaking parameter, substantially accelerating mixing. The method also rigorously characterizes the range of asymmetric target states for which effective acceleration is guaranteed.