Quantum control for time-dependent noise by inverse geometric optimization

Quantum systems are exceedingly difficult to engineer because they are sensitive to various types of noises. In particular, time-dependent noises are frequently encountered in experiments but how to overcome them remains a challenging problem. In this work, we propose a flexible robust control technique to resist time-dependent noises based on inverse geometric optimization working in the filter-function formalism. The basic idea is to parameterize the control filter function geometrically and minimize its overlap with the noise spectral density. This then effectively reduces the noise susceptibility of the controlled system evolution. We show that the proposed method can produce high-quality robust pulses for realizing desired quantum evolutions under realistic noise models. Also, we demonstrate this method in examples including dynamical decoupling and quantum sensing protocols to enhance their performances.