Error-rate-agnostic decoding of topological stabilizer codes

Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve balance between logical failure rates and number individual error constituent qubits. High-threshold maximum-likelihood decoders require an explicit model for Pauli errors decode a specific syndrome, whereas lower-threshold heuristic approaches such as minimum weight matching are "error agnostic". Here we consider intermediate approach, formulating decoder that depends on bias, i.e., relative probability phase-flip bit-flip errors, but is agnostic rate. Our based counting effective most likely chains in each equivalence class given syndrome. We use Metropolis-based Monte Carlo sampling explore space find unique chains, efficiently identified using hash table. Using error-rate invariance can sample effectively at rate which higher than physical without need "thermalization" different classes. Applied surface code XZZX code, matches moderate sizes or low rates. anticipate that, because compressed information content per it be taken full advantage combination with machine-learning methods extrapolate Carlo-generated data.