Error-rate-agnostic decoding of topological stabilizer codes

TL;DR

This paper introduces an error-rate-agnostic decoder for topological stabilizer codes that leverages error bias information without requiring explicit error rates, using Monte Carlo sampling to efficiently identify likely error chains.

Contribution

The authors develop a novel decoder that depends on error bias but is agnostic to error rate, improving decoding efficiency for topological codes.

Findings

Matches maximum-likelihood decoders for moderate code sizes

Operates effectively at higher error rates without thermalization

Potentially enhances decoding with machine learning integration

Abstract

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