Introduction to open quantum systems IV

Laurent Sanchez-Palencia

Laurent Sanchez-Palencia

Laurent Sanchez-Palencia

Xiaohan Dan, Saurabh Shivpuje, Yuchen Wang +9 more

Energy and charge transfer processes, which are central to photosynthesis, catalysis, and molecular electronics, are governed by quantum dynamics in contact with complex environments. Interactions with surrounding degrees of freedom give rise to dissipation, decoherence, and energy exchange, shaping the mechanisms that determine chemical reactivity and transport phenomena. In Part IV of the QFlux tutorial series, we extend our study of quantum dynamics to open quantum systems, where time evolution is intrinsically non-unitary. Using the Lindblad master equation as a unifying and practical framework, we show how environmental effects can be modeled, simulated, and visualized with QFlux , an open-source platform that bridges classical and quantum computation. The tutorial presents the theoretical foundations of open-system dynamics, constructs the Lindblad propagator, and implements representative simulations ranging from spin models to chemically relevant double-well potentials. Special attention is given to dilation methods, which embed non-unitary dynamics within an enlarged unitary space through ancillary qubits, enabling open-system simulations on quantum hardware. This installment provides both conceptual insight and computational methodology for exploring dissipative quantum dynamics, laying the groundwork for subsequent parts addressing variational, non-Markovian approaches.

Janik Wolters

In Part I, several fundamental results of theoretical quantum optics and light-matter interaction are elaborated. It provides all necessary theoretical background to understand the physics of the single quantum emitters introduced in Part II and later on coupled systems discussed in Part IV.

Fabrizio Minganti, Alberto Biella

This text is a short introduction to the physics of driven-dissipative many-body systems, focusing on a few selected topics. Beyond its more ``historical'' interest in the study of atomic physics and quantum optics, presently the modeling and studying dissipative phenomena in open quantum systems is pivotal to understanding quantum hardware platforms. While the lack of a thermodynamic potential for these out-of-equilibrium open systems makes it theoretically challenging to investigate their physics, at the same time it allows going beyond the thermodynamic paradigms and investigating new and exotic phenomena. We will focus on one of the simplest, yet most effective, descriptions of open quantum systems, namely the (Gorini-Kossakowski-Sudarshan-) Lindblad master equation. This phenomenological approach describes quantum systems that weakly interact with their surrounding environment. Although many of the results derived below will apply to any quantum system, we will focus in particular on bosonic/spin systems.