Effective master equation modeling of correlated noise

Developing tools that allow for accurate descriptions of driven quantum dynamics in the presence of non-Markovian noise is essential for understanding and possibly mitigating decoherence in realistic devices. This problem is challenging even in the case where the noise is classical and Gaussian. We recently introduced an approach based on a generalized cumulant expansion, which yields a time-local pseudo-Lindblad master equation (PLME)[1]. These equations have a form reminiscent of standard Lindblad master equations, except decoherence rates are time-dependent and possibly negative. Here, we discuss how the PLME approach can be extended to describe more complicated setups involving many interacting qubits, subject to noise that is both correlated in space and time. We show how the interplay of these elements leads to a number of phenomena that are missed if one makes standard Markovian approximations. We discuss applications to understanding the impact of 1/f dephasing noise on the performance of superconducting quantum circuit architectures, as well as extensions to include quantum noise effects.