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Definition of distance $d$:

$d$ of $T(S)$ is the weight of the smallest Pauli operator $N$ in $N(S)$ \ $S$. $S$ is the stabilizer, $T(S)$ is the corresponding QECC, and $N(S)$ are all errors commute with elements in S.

I am confused about this definition, especially about the "weight".

I'd really appreciate it if someone could help clarify it!

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The weight of an error in QEC is the number of qubits, on which the error acts non-trivially. For example, the error $X\otimes Y\otimes Id$ has weight two. The weight is important, because usually we know that a code can correct errors up to some weight.

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  • $\begingroup$ That is a really concise and great answer! Thanks!! $\endgroup$
    – Tianyi
    Sep 9 at 7:13

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