Half-Integer Spectral Zeros for Leakage Suppression in Fast Transmon Pulses

Abstract

A flat-top transmon pulse with cosine ramps has exact spectral zeros at half-integer values of ramp duration times anharmonicity, (\tau|\alpha|=n+1/2), which predict endpoint-leakage minima in the weak-drive regime. For any self-similar one-scale envelope (\Omega(t)=\Omega_0 f(t/\sigma)), the non-adiabaticity parameter is exactly degenerate with pulse area, (\eta_{\rm ref}\theta=C_{\rm shape}); an independent ramp timescale (\tau) is therefore required. The Fourier amplitude of the resulting envelope at the anharmonicity vanishes at (\tau|\alpha|=n+1/2) through destructive interference between the rising and falling edges, independently of plateau length and total pulse duration. Dynamically, the endpoint-leakage amplitude is perturbatively determined by the Fourier component of the envelope weighted by the instantaneous excited-state amplitude. This weighting removes a second, plateau-derived family of envelope zeros not followed by the dynamics. Four-level Duffing simulations using parameters representative of IBM Heron r2 devices collapse the minima onto the half-integer sequence for six pulse durations from 50 to 100 ns, with an RMS deviation of 0.034 in (\tau|\alpha|). For four durations resolved on a finer grid, first-order population weighting reduces the positional deviation from 0.0234 to 0.0096. The competing plateau condition does not collapse the data. The residual weak-drive displacement from the half-integers is captured by the population-weighted correction.