  We consider a class of multi-qubit dephasing models that combine classical
noise sources and linear coupling to a bosonic environment, and are controlled
by arbitrary sequences of dynamical decoupling pulses. Building on a general
transfer filter-function framework for open-loop control, we provide an exact
representation of the controlled dynamics for arbitrary stationary non-Gaussian
classical and quantum noise statistics, with analytical expressions emerging
when all dephasing sources are Gaussian. This exact characterization is used to
establish two main results. First, we construct multi-qubit sequences that
ensure maximum high-order error suppression in both the time and frequency
domain and that can be exponentially more efficient than existing ones in terms
of total pulse number. Next, we show how long-time multi-qubit storage may be
achieved by meeting appropriate conditions for the emergence of a fidelity
plateau under sequence repetition, thereby generalizing recent results for
single-qubit memory under Gaussian dephasing. In both scenarios, the key step
is to endow multi-qubit sequences with a suitable displacement anti-symmetry
property, which is of independent interest for applications ranging from
environment-assisted entanglement generation to multi-qubit noise spectroscopy
protocols.
