The book can be considered as a conceptual integration of two parallel emergent streams: quantum technology and brain-inspired computing, from the perspective of information processing. The book addresses the current issues associated with the non-equilibrium processes involved in either stream that cannot be explained by conventional semi-classical or equilibrium- statistical models. The purpose of this book is to provide a detailed explanation of how the non-equilibrium Green's function (NEGF) method can be utilized to develop quantum and brain-inspired device simulators. The book covers the fundamental concepts of NEGF and its relevance in describing communication between the quantum and classical world. It also outlines its applications in modeling quantum transport in ultra-scaled devices such as nano- MOS/MOSFETs, photodetectors, solar cells, LEDs, lasers, and metasurfaces. Additionally, the book discusses non-conventional phenomena related to phonons and electron spin in quantum devices. The NEGF method presented in the book is also used to model qubit operations as-well-as functional connectivity in brain and neuromorphic computing devices. Finally, based on the physical insights behind NEGF formalism, the book proposes exploring fractional dimensions to offer a new vision of the real world.