Compressed-sensing Lindbladian quantum tomography with trapped ions

Abstract Characterizing the dynamics of quantum systems is a central task for the development of quantum information processors (QIPs). It serves to benchmark different devices, learn about their specific noise, and plan 
the next hardware upgrades. However, this task is also very challenging, for it 
requires a large number of measurements and time-consuming classical processing. 
 Moreover, when interested in the time dependence of the noise, there is an additional overhead 
since the characterization must be performed repeatedly within the time interval of interest. To overcome this limitation while, at the same time, ordering the learned sources of noise by their relevance, 
we focus on the inference of the dynamical generators of the noisy dynamics using Lindbladian quantum tomography (LQT). 
We propose two different improvements of LQT that alleviate previous shortcomings. In the weak-noise regime of current QIPs, 
we manage to linearize the maximum likelihood estimation of LQT, turning the constrained optimization into a convex problem to reduce the classical computation cost and to improve its robustness. Moreover, by introducing compressed sensing techniques, we reduce the number of required measurements without sacrificing accuracy. 
To illustrate these improvements, we apply our LQT tools to trapped-ion experiments of single- and two-qubit gates, advancing in this way the previous state of the art.