Open-loop quantum control of small-size networks for high-order cumulants and cross-correlations sensing.

Quantum control techniques are one of the most efficient tools for attaining high-fidelity quantum operations and a convenient approach for quantum sensing and quantum noise spectroscopy. In this work, we investigate dynamical decoupling while processing an entangling two-qubit gate based on an Ising-xx interaction, each qubit affected by pure dephasing classical correlated 1/f-noises. To evaluate the gate error, we used the Magnus expansion introducing generalized filter functions that describe decoupling while processing and allow us to derive an approximate analytic expression as a hierarchy of nested integrals of noise cumulants.