Quantum Computing is an ever-increasing field of interest both from a conceptual and applied standpoint. Quantum Computing, belonging to the so called "Quantum Information Science", is founded on the principles of Quantum Mechanics and Information Science. Quantum Mechanics has radically changed our vision and understanding of the physical reality and has had also an enormous technological and societal impact. On the other hand, the developing of Information Theory, including computer science and communications theory, made possible the information "revolution" which had a deep impact on our everyday life. Quantum Computing then relates to the possibility to represent, process and manipulate information by using the principles of quantum mechanics. Apart the theoretical importance of quantum computing to further understand the quantum mechanical behavior of physical systems and the physical foundation of information itself at the most elementary level, probably the most interesting feature of Quantum Computing is related to the possibility to design and realize an actual quantum computer which processes information in the form of quantum-bits or qubits. The great interest of scientific community in the realization of such devices mainly concerns the common believe they could be enormously faster than their classical counterparts so allowing their employment in all the applied fields where computational power is a key feature. Furthermore, the study of Quantum Computing, both at the physical and computational level, would be very important for a deeper understanding of the quantum behavior of a very wide range of physical systems including condensed matter, living systems, elementary particles, astrophysical structures and so on. Despite the general theoretical basis of quantum computing are sufficiently understood, the actual realization of a general - purpose and really usable quantum computer has posed great difficulties so far, mainly related to the issue of "quantum decoherence", the computational speed and scalability many of which still remain substantially unsolved. This volume doesn't mean to represent a complete or a beginner guide to Quantum Computing but has the aim to present some of its most interesting and fascinating developments in different frontier areas related to both theoretical and applied aspects, such, for example, the possibility to realize a quantum superfast "hypercomputing" system using water molecules as physical substrate to process, storage and retrieve information; the connection between quantum computers and quantum gravity; the development of an "instantaneous quantum computer algorithm"; the realization of a universal quantum computer, of a brain-like quantum supercomputer and many others frontiers topics. The target audience of this book is then composed by scientists and researchers interested in the most advanced theoretical and applied developments of quantum computation and quantum information.