Definition 2 on page 20 in Daniel Gottesman's An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation states that a nondestructive logical measurement procedure is fault tolerant if

the total number of errors in the incoming state and measurement gadget is at most t, then we should get the same result out of the real gadget as if we had performed ideal decoding on the incoming state and measured the decoded qubit.

Are there procedures known that satisfy this definition for arbitrary distance?

I am aware of the distance 3 procedure in section 7.4 of Quantum accuracy threshold for concatenated distance-3 codes. It is straightforward to extend this to higher distance.

I am also aware of the code specific measurement procedures in section 10 of Short Shor-style syndrome sequences.



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