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We introduce a quantum control protocol that produces smooth, experimentallyimplementable control sequences optimized to combat temporally correlated noisefor single qubit systems. The control ansatz is specifically chosen to be afunctional expansion of discrete prolate spheroidal sequences, a discrete timebasis known to be optimally concentrated in time and frequency, and quiteattractive when faced with experimental control hardware constraints. Weleverage the filter function formalism to transform the control problem into afilter design problem, and show that the frequency response of a quantum systemcan be carefully tailored to avoid the most relevant dynamical contributions ofnoise processes. Using gradient ascent, we obtain optimized filter functionsand exploit them to elucidate important details about the relationship betweenfilter function design, control bandwidth, and noise characteristics. Inparticular, we identify regimes of optimal noise suppression and in turn,optimal control bandwidth directly proportional to the size of the frequencybands where the noise power is large. In addition to providing guidingprinciples for filter design, our approach enables the development of controlsthat simultaneously yield robust noise filtering and high fidelity single qubitlogic operations in a wide variety of complex noise environments.

Optimally Band-Limited Noise Filtering for Single Qubit Gates