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The threshold theorem states that any abstract circuit in BQP can be computed by another polynomial-depth circuit that succeeds in the presence of noise. The original construction from 1996 requires paying a poly-log factor of depth. Is it possible to reduce this to a constant overhead factor? What are the known lower bounds regarding fault-tolerant computation?

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    $\begingroup$ It looks like it's probably possible: arxiv.org/abs/1310.2984 (this requires a family of codes with the right properties. There's been a lot of progress on these types of code recently, although I don't know if they quite match up with the requirements of the paper.) $\endgroup$
    – DaftWullie
    Commented May 18, 2023 at 14:44

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