Enhanced quantum signal control and sensing under multicolored noise via generalized filter function framework

The field of quantum signal control and sensing encounters challenges due to various forms of time-dependent noise. We introduce a generalized filter-function framework that treats noise coupling strength as a tunable control parameter, enabling target noise suppression across user-defined frequency bands. By optimizing this generalized filter function, we design band-selective control pulses that achieve more than $0.999$ fidelity of single- and two-qubit gates under strong noise with diverse spectral profiles. We further extend the method to selectively enhance the signal-to-noise ratio for quantum sensing of AC signals with an enhanced precision of up to $12.58$ dB. The resulting control pulses are experimentally feasible, offering a practical pathway toward robust quantum operations and high-precision sensing under spectrally complex noises.