Decoding syndrome measurements in a distance-three surface code

Successful and close-to-optimal decoding of error syndromes in the surface code requires a thorough understanding of the errors occurring while executing error correction cycles. Only then can a decoder associate each error syndrome with its most likely error class. Here we present a scheme based on the correlation analysis by Spitz et al. [1] to extract physical error probabilites per cycle directly from surface code experiments. We use the measured error rates to optimally set the weights in a minimum-weight-perfect-matching decoder used to correct errors in our quantum memory experiments [2]. Analyzing beyond-nearest-neighbor correlations between syndrome elements allows us to extend our understanding of different error sources.

[1] Spitz et al., Adv. Quantum Technol. 1, 1800012 (2018)

[2] Krinner et al., Nature 605, 669 (2022)