Fast interactions in driven-dissipative quantum systems: Too much of a good thing?

Realizing strong light-matter interactions is the foundational principle that enables all critical quantum information functionalities, be it quantum gates, qubit readout or quantum error correction. The insidious interplay of time-dependent driving, dissipation and strong coupling, however, poses new challenges both in terms of controlling these systems with high fidelity, as well as predicting their dynamics. In this talk, I will discuss our recent theoretical progress in this direction and some associated cautionary tales for theorists and experimentalists alike. First, I will discuss how strong coupling can conspire with dissipation and lead to non-trivial interactions between seemingly independent and even orthogonal decoherence channels. Using a new framework called DISCO (for Dissipation-Incorporated Self -consistent COarse graining), we predict a host of new Purcell and Zeno modifications that can explain non-QND and non-Markovian effects encountered in cQED-type architectures. Notably, we find that these new error channels can even limit the success of usual error correction schemes applied in such settings. Next, I will present an analytical framework based on symplectic transformations to incorporate the effects of strong driving nonperturbatively. In addition to deconstructing different drive-mediated interactions, such as cross-Rabi driving, parametric swaps etc., this method allows to isolate the terms responsible for leakage and nonlinear crosstalk in distinct superconducting circuit geometries. Finally, I will discuss how these theoretical insights can guide new strategies for implementing quantum control and unraveling novel out-of-equilibrium quantum phenomena in strongly interacting quantum matter.