Quantum Gates Robust to Secular Amplitude Drifts

Quantum gates are typically vulnerable to imperfections in the classical control fields applied to physical qubits to drive the gates. One approach to reduce this source of error is to break the gate into parts, known as textit{composite pulses} (CPs), that typically leverage the constancy of the error over time to mitigate its impact on gate fidelity. Here we extend this technique to suppress textit{secular drifts} in Rabi frequency by regarding them as sums of textit{power-law drifts} whose first-order effects on over- or under-rotation of the state vector add linearly. We show that composite pulses that suppress the power-law drifts $t^p$ for all $p leq n$ are also high-pass filters of textit{filter order} $n+1$ cite{ball_walsh-synthesized_2015}. We present sequences that satisfy our proposed textit{power law amplitude} $text{PLA}(n)$ criteria, obtained with this technique, and compare their simulated performance under time-dependent amplitude errors to some traditional composite pulse sequences. We find that there is a range of noise frequencies for which the $text{PLA}(n)$ sequences provide more error suppression than the traditional sequences, but in the low frequency limit, non-linear effects become more important for gate fidelity than frequency roll-off. As a result, the previously known $F_1$ sequence, which is one of the two solutions to the $text{PLA}(1)$ criteria and furnishes suppression of both linear secular drift and the first order nonlinear effects, is a better noise filter than any of the other $text{PLA}(n)$ sequences in the low frequency limit.