Exact Solutions of Interacting Dissipative Systems via Weak Symmetries

As superconducting qubit-based quantum information processors continue to improve, a better understanding of strongly-interacting dissipative quantum models is required to accurately model such systems. Exact solutions in such instances however are few and far between; adding dissipation to even the simplest closed-system Hamiltonian often means resorting to numerics or employing unjustified approximations.

In this talk, I show how so-called weak symmetries can be used to analytically diagonalize a large class of strongly-interacting dissipative Markovian Lindblad master equations which are relevant to superconducting qubits. That is, one can obtain a quantitative understanding of all characteristic decay rates and describe the exact evolution of an arbitrary initial state.

The method effectively implements an unusual yet exact mean-field decoupling, allowing one to fully describe the dynamics and dissipative spectrum. I will discuss how these solutions also provide an intuitive picture of the dynamics in these models. Finally, I will briefly explore how this approach can be used as a starting point to perform perturbative analyses to more complex systems where, crucially, the non-linearities are included in the unperturbed theory.