Unitary Dynamics for Open Quantum Systems With Density-Matrix Purification
Luis Delgado Granados, University of Chicago
Accurate modeling of open quantum systems (OQS) requires tackling different challenges, such as non-unitary dynamics, which significantly increases the complexity of computational approaches, and systems strongly correlated with their environments, being an open question in the field of how to model them. In this work, we further develop an OQS theory based on density-matrix purification, which recovers a unitary description of dynamics by entangling a maximally mixed system with an environment of equal dimension as the system. Additionally, by creating an entangled representation of the system-environment, it allows for the modeling of strongly correlated system-environment. We first establish the connection between the density-matrix purification and the conventional approaches to OQS. We then demonstrate how the purification theory can be used as a stand-alone theory by building the system-environment interaction from a set of design principles. By using model systems, we illustrate that the purification approach takes us beyond the complete positivity condition and that it can model both Markovian and non-Markovian dynamics. Finally, we implement the density-matrix purification on a quantum simulator, demonstrating its ability to map the non-unitary dynamics of OQS onto the unitary framework of quantum computers.