= Operator-norm distance between unitary gates
{title2=$d_{\mathrm{op}}(U,V)=\|U-V\|_{\mathrm{op}}$}
The largest <pure-state norm distance> between outputs of two <unitary operators> on the same normalized input. By definition of the <operator norm>, it is $\sup_{\|\psi\|_2=1}\|(U-V)|\psi\rangle\|_2$. If it is at most $\varepsilon$, every input is approximated to that accuracy. A version disregarding the operation's <global phase> minimizes $\|U-e^{i\gamma}V\|_{\mathrm{op}}$ over one common $\gamma$. Error in a finite <quantum circuit> accumulates at most additively by the <quantum circuit gate-error telescoping bound>.
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