Description
In this talk, I will present a framework to study sensitivity to a given class of perturbations in multiqubit systems with and without control. I will start by introducing the notion of universal robustness for general quantum systems and its connection to unitary designs and robust quantum control. I will then focus on multiqubit systems and the study of sensitivity to classes of perturbations, e.g., one-body, two-body, etc. I will show that the degree of robustness to a multi-body perturbation is determined by the operator-growth properties of the time-evolution operator; in particular, persistent and extensive spreading of U(t) in the Pauli basis is required to achieve robustness against any single-body error. We prove that there is no time-independent Hamiltonian that is universally robust, but also that there exist N-qubit Hamiltonians that are robust against any single- or two-body perturbation. By leveraging the concept of k-uniform states, we show explicitly how these Hamiltonians can be constructed and discuss their application to dynamical decoupling protocols requiring no active control. We further discuss how this dynamical sensitivity is related to a generalized version of the spectral form factor.