When we use surface code to detect and correct errors, we can track the errors in software and change the computation results accordingly. So why do we need real-time feedback on decoding results? Are there any logical operations that demand real-time feedback of the previous decoding results to implement correctly? If it is, what are they?

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    $\begingroup$ "Need" is in the eye of the beholder, but you're obligated to keep track of the error history until you correct the errors, which adds classical space overhead on the order of (runtime / surface code cycle time) * qubit count. Now (1) consider current application estimates for runtime * qubit count (e.g., search in arxiv.org/pdf/1905.09749.pdf for "megaqubitdays") and (2) recall that surface code cycle time is expected to be on the order of microseconds. Together, these give a back-of-the-envelope estimate of syndrome data storage size — I get ~50 petabytes when factoring RSA 2048. $\endgroup$ Oct 14 '21 at 21:45
  • $\begingroup$ It's also worth mentioning that the amount of processing needed to install a correction grows as it lingers. The exact rate of growth depends on many factors, so is hard to enunciate — but in any case sooner is better. $\endgroup$ Oct 15 '21 at 16:58
  • $\begingroup$ Thanks for your ideas. I also wonder that whether we need real-time feedback in principle when we do logical operations. For example, when we want to implement a logical T we need to decide whether to add logical S according to logical measurement results. Then we need to finish decoding before outputting the correct measurement results. $\endgroup$
    – Inm
    Oct 17 '21 at 2:23

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