= Graph-state preparation of a computational-basis input
{title2=$|+\rangle\longmapsto X^s|0\rangle$}
A two-vertex <graph state> starts with two $|+\rangle$ states joined by a <Controlled-Z gate>. Measuring the first vertex in the $X$ basis leaves the second in $X^sH|+\rangle=X^s|0\rangle$, where $s$ is the measurement outcome. Thus a known zero input can be supplied to a measurement wire using only a graph-state resource and a known <Pauli frame>. This preparation link precedes the links implementing the desired logical <J gate>; later measurement angles and output-bit corrections absorb its byproduct.
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