CMT Forum: Linnea Grans-Samuelson

The optimal thresholds of quantum error-correcting stabilizer codes have early on been related to order-disorder phase transitions within disorderered statistical mechanics models of Random Bond Ising-type. In this talk, I present a framework for obtaining the full logical error curves for two families of decoding strategies: maximum partition function decoders and probabilistic partition function decoders. Maximum likelihood (optimal) decoding is a member of the former family, while maximum probability (MP) decoding is a member of the latter. The logical error rates for the two families are given by two ratios of partition functions, and estimating the error rates through these ratios is expected to be generally more sample-efficient than estimating the error rates by counting the number of failures of the corresponding decoders. Based on the distinction between the two decoders, I discuss the possibility that some stabilizer codes may map to models with a maximum partition function decodability boundary that is distinct from the phase boundary. At zero temperature, the difference between the two ratios measures to what degree MP decoding can be improved by accounting for degeneracy among maximum probability errors, through methods such as ensembling. The presentation focuses on the example of the toric code under uniform and non-uniform bitflip noise.