Degeneracy-aware decoders

[Krastanov]

From Henry Makhanov, with comments by me inline as quote blocks:

Count Degenerate Logical Operators Per Syndrome Pair (Implement count_logical_paths)

For a given syndrome pair (two defects), count the number of equivalent paths (logical or stabilizer-equivalent) between them.

function count_logical_paths(code::AbstractECC, defect_i::Int, defect_j::Int)
    # Enumerate all minimum-weight error chains between i and j,
    # count how many are logically equivalent (modulo stabilizers)
    return Int
end

Modify MWPM Edge Weights Using Degeneracy Heuristics (Implement degeneracy_weighted_graph)

Adjust decoder edge weights using:

Standard: wᵢⱼ = -log(pᵢⱼ)

Degeneracy-aware: wᵢⱼ = -log(pᵢⱼ * Dᵢⱼ)
where Dᵢⱼ is the degeneracy factor (e.g., number of equivalent minimal chains between i and j)

function degeneracy_weighted_graph(code::AbstractECC, noise::Dict, degeneracy_map::Dict)
    # Build weighted graph with weights adjusted using degeneracy
    return WeightedGraph
end

Modular Compatibility with Existing Decoders and with Weight adjustments (Implement total_matching_weights)

Make sure that these features work with all existing decoders defined in ecc/codes.

I think crucial for my vision is to make points 4 and 5 so that the weights would be defined for decoders like MWPM as:
w_ij total=−log(p_ij⋅D_ij)=−log(p_ij)−log(D_ij)

function total_matching_weights(
    noise_map::Dict{Int, PauliNoise},
    code::AbstractECC,
    degeneracy_map::Dict{Tuple{Int,Int}, Int}
)
    # p_{ij} from noise_map (from point 3)
    # D_{ij} from degeneracy_map (from point 4)
    # Return edge list for PyMatching
end