Monte Carlo sampling for optimal decoding of arbitrary topological orders

Determine whether Monte Carlo sampling of the constrained subspace of anyon-string configurations, using local updates and configuration weights, provides a realistic route to optimal decoding for arbitrary topological orders with anyon-syndrome measurements.

Background

The ILP formulation can be interpreted as a constrained classical statistical-mechanics model whose binary variables represent anyon-string configurations. The paper suggests sampling admissible configurations according to their weights as an alternative to deterministic minimum-weight optimization.

Although the authors note that the computational complexity of such sampling schemes may scale polynomially with code distance, they also expect the schemes to be slow in practice. Whether this approach can achieve practically useful optimal decoding remains explicitly unresolved.