= J-gate phase-error operator norm
{c}
{title2=$\|J(\alpha+\delta)-J(\alpha)\|=2|\sin(\delta/2)|$}
The <J gate> is $J(\alpha)=HP(\alpha)$, where $P(\alpha)=\operatorname{diag}(1,e^{i\alpha})$: the <phase gate> acts first and the <Hadamard gate> acts second. Unitary invariance of the <operator norm> reduces its angle error to the single nonzero diagonal difference of the <phase gate>. Its norm is $|e^{i\delta}-1|=2|\sin(\delta/2)|\leq|\delta|$. The <quantum circuit gate-error telescoping bound> then makes an angle tolerance of $\epsilon/k$ sufficient for $k$ such imperfect gates and exact other gates.
Back to article page
