Experimentally informed decoding of stabilizer codes based on syndrome correlations

High-fidelity decoding of quantum error correction codes relies on an accurate experimental model of the physical errors occurring in the device. 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 an 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mover accent="true"> <a:mi>Y</a:mi> <a:mo>̂</a:mo> </a:mover> </a:math> errors, hook errors, multiqubit errors, and leakage, in addition to standard Pauli <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mover accent="true"> <c:mi>X</c:mi> <c:mo>̂</c:mo> </c:mover> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mover accent="true"> <e:mi>Z</e:mi> <e:mo>̂</e:mo> </e:mover> </e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mover accent="true"> <g:mi>Y</g:mi> <g:mo>̂</g:mo> </g:mover> </g:math> error channel, based on correlating the X- and Z-type error syndromes, can be exploited to enhance matching decoding. Furthermore, we find correlated errors that flip many syndrome elements over up to eight cycles, potentially caused by leakage of the data qubits out of the computational subspace. The presented method provides the tools for accurately calibrating a broad family of decoders, beyond the minimum-weight perfect matching decoder, without relying on prior knowledge of the error model.