Simulating and understanding quantum processes using tensor networks

Abstract

Simulation of quantum processes is essential to both furthering our understanding of the microscopic world and also in developing quantum technologies. For accuracy we must take into consideration the environment in which they take place. In this thesis we begin by introducing an existing method that utilises tensor networks to efficiently represent the time non-local evolution of the system induced by interaction with its environment. Previously reliant on a linear interaction and a Gaussian environment, it is presented with no assumptions made on the form of interaction or environment statistics. The versatility is then showcased by first simulating the dynamics of a system coupled to a structured environment before then considering a pair of spatially separated systems coupled to the same environment. Here we see that the separation can be tuned to screen the interaction with dominant modes in the environment. Moving beyond system dynamics we show how correlation functions can be efficiently calculated and used to infer the dynamics of the bath. This result is then applied to study the dynamics of heat exchange between a system and regions of the environment; in particular a time dependent drive is employed to move heat between specific regions as desired. Finally, we see how the dynamics of a dimer coupled to both photons and phonons can be exactly captured and its non-equilibrium steady state is explored in all coupling regimes. This required extending the method to be able to combine the memory effects from each environment. The occurrence of population inversion is confirmed at weak light-matter coupling and then shown to disappear as the coupling is increased before entering a regime characterised by quantum Zeno physics.