Modeling non-Markovian dynamics with augmented CPTP maps

Markovian quantum processes on qubits can be perfectly described with completely-positive, trace-preserving (CPTP) maps. However, real physical systems are replete with non-Markovian effects. Trapped ions experience heating, microwave sources display power instabilities, and resonators take time to relax. Fluctuating magnetic fields display large spatial correlations, qubits experience leakage, and quantum gates that occur early in a circuit can impact the performance of those occurring later. CPTP maps on qubits capture none of these memory effects. In this talk, we propose a family of augmented CPTP maps that enable simple models of a wide variety of non-Markovian dynamics. We provide a number of numerical examples demonstrating that that these maps are easy to construct and interpret. Furthermore, we show that we can estimate the parameters of these maps from experimental data.