Why real-time decoding is necessary for non-Clifford gate?

Why real-time decoding is necessary for non-Clifford gate? Ask Question Asked 2 days ago Modified 2 days ago Viewed 89 times 3 I'm trying to understand why real-time decoding is necessary. This post and other sources say that real-time decoding is not required for Clifford circuits because we can move the errors to the end and decode in post-processing. It is not clear to me why real-time decoding is necessary for non-Clifford (T) gates. It seems it is because the decoding result is required to decide whether to apply the S gate or not. However, the S gate can also be commuted to the end of the circuits and doesn't need to be applied immediately. In the other post, it said the decoding results are required for the next "decoding-dependent gates". However, it didn't define what decoding-dependent gates are. Can anyone help explain why real-time decoding is necessary for non-Clifford (T) gates and what the definition of " decoding-dependent gates " is (what QEC operations need the previous decoding results)? error-correctionsurface-codedecoding Share Improve this question Follow asked 2 days ago Amanli 874 4 bronze badges 2 If you commute the S gate to the end of the circuit, it becomes something huge and ugly involving many, many Clifford operations. If you commute a Pauli to the end of a circuit, it becomes another Pauli. –  Jahan Claes Commented 2 days ago @JahanClaes Do you think that's the only reason why non-Clifford gate requires real-time decoding? Based on arxiv.org/pdf/1808.02892, all Clifford gates should be commuted to the end, leaving only pauli product rotations. –  Amanli Commented yesterday Add a comment Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. 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