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 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 secular drifts in Rabi frequency by regarding them as sums of power-law drifts whose first-order effects on over- or under-rotation of the state vector add linearly. Power-law drifts have the form $t^p$ where $t$ is time and the constant $p$ is its power. We show that composite pulses that suppress all power-law drifts with $p \leq n$ are also high-pass filters of filter order $n+1$ arXiv:1410.1624. We present sequences that satisfy our proposed power-law amplitude criteria, $\text{PLA}(n)$, 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 sharper noise filter than any of the other $\text{PLA}(n)$ sequences in the low frequency limit.