Filter Function Tailored Noise-Optimized Single Qubit Gates

Noise suppression protocols represent a class of techniques that are meant to reduce gate error rates via specially designed control sequences. Here, we discuss a protocol that optimizes smooth control sequences to combat temporally-correlated noise, a class of noise that can be detrimental to quantum error correction. The control ansatz is specifically chosen to be a functional expansion of Slepians, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of the noise processes. Using gradient ascent, we obtain optimized filter functions and investigate the relationship between filter function design, control bandwidth, and noise characteristics. Even in the presence of multi-axis correlated noise, we show that as long as the noise spectral density is sufficiently weak over a range of frequencies, it is possible to generate control sequences that yield highpass or bandpass filter functions, and simultaneously produce high fidelity, arbitrary single qubit gate operations.