Efficient approximate anyonic symmetry learning for larger error thresholds

Determine whether Approximate Anyonic Symmetry Learning over finite abelian groups can be solved with high probability for approximation thresholds larger than O(1/log |G|), ideally for every threshold below a fixed constant.

Background

The paper defines Approximate Anyonic Symmetry Learning by asking for the set of group elements g satisfying |Tr(R(g)ρ)| ≥ 1 − ε₁, where G is a group, R is a representation, ρ is a state, and ε₁ is an approximation threshold. It observes that the existing algorithm handles finite abelian groups when ε₁ = O(1/log |G|), but leaves the behavior at larger error thresholds unresolved.