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تسجيل مستخدم جديدAll the stabilizer codes of distance 3
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We give necessary and sufficient conditions for the existence of stabilizer codes $[[n,k,3]]$ of distance 3 for qubits: $n-kge lceillog_2(3n+1)rceil+epsilon_n$ where $epsilon_n=1$ if $n=8frac{4^m-1}3+{pm1,2}$ or $n=frac{4^{m+2}-1}3-{1,2,3}$ for some integer $mge1$ and $epsilon_n=0$ otherwise. Or equivalently, a code $[[n,n-r,3]]$ exists if and only if $nleq (4^r-1)/3, (4^r-1)/3-n otinlbrace 1,2,3rbrace$ for even $r$ and $nleq 8(4^{r-3}-1)/3, 8(4^{r-3}-1)/3-n ot=1$ for odd $r$. Given an arbitrary length $n$ we present an explicit construction for an optimal quantum stabilizer code of distance 3 that saturates the above bound.
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