Experimentally Informed Decoding of Stabilizer Codes Based on Syndrome Correlations

Because error probabilities can depend on the context of the applied operations, the error model is ideally calibrated using the same circuit as is used for the error correction experiment. Here, we present an experimental approach guided by a novel analytical formula to characterize the probability of independent errors using correlations in the syndrome data generated by executing the error correction circuit.

Using the method on a distance-three surface code, we analyze error channels that flip an arbitrary number of syndrome elements, including Pauli Y errors, hook errors, multi-qubit errors, and leakage, in addition to standard Pauli X and Z errors. We use the method to find the optimal weights for a minimum-weight perfect matching decoder without relying on a theoretical error model. Additionally, we investigate whether improved knowledge of the Pauli Y error channel, based on correlating the X- and Z-type error syndromes, can be exploited to enhance matching decoding.