= Three-pulse amplitude-error compensation
{title2=$1-\mathcal F=3\pi^4\epsilon^4/128+O(\epsilon^6)$}
For chronological equatorial rotations $R_\phi(\pi)R_{2\phi}(\pi)R_\phi(\pi)$, the ideal propagator is $iX$. If all pulse angles have the same fractional error $\epsilon$, choose $\cos\phi=-1/2$ to cancel the quadratic term of the <trace-overlap gate fidelity>. With $x=\pi\epsilon/2$, its exact fidelity is $|\cos x(1+\sin^2x/2)|$, whose leading infidelity is $3x^4/8$. This correction compensates a systematic amplitude error, not arbitrary axis or timing errors.
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