Color code decoder with confidence reporting for efficient escape via pure color-code growth

Develop an accurate color code decoder that provides calibrated confidence (e.g., complementary gap) estimates suitable for fine-grained postselection during code growth, enabling the escape stage to proceed by growing the color code into larger distances without grafting into a surface code.

Background

The authors initially aimed to escape by simply growing the color code to larger distance, but found their current decoder (Chromobius) insufficiently accurate and lacking confidence outputs needed for efficient postselection. As a result, they devised a more complex grafting procedure into a surface code.

A decoder that can both accurately predict and report confidence would allow a simpler, purely color-code growth escape strategy, potentially reducing complexity and costs.