Abstract This chapter introduces the basic concepts of quantum information processing with superconducting quantum circuits. It starts with a demonstration of how,in these electrodynamic systems, both the superconducting gap and the long-range Coulomb interactions contribute to the existence of collective modesthat have extremely low dissipationand that can be quantized. The chapter also gives in-depth coverage of quantum harmonic oscillators in all their glory from various perspectives. Superconducting qubits are then introduced, starting with the fundamental theory of the Josephson effect and moving on to a presentation of the variety of existing superconducting qubits. Particular attention is given to the dispersive readout of qubits through their interaction with a cavity into which flying modes can be scattered. Finally, the opportunities offered for quantum information processing by employing the cavity as a quantum bus are presented.
This book adopts a novel, physics-first approach to quantum measurement, using physical experiments as the basis to describe the underlying mathematical formalism. Topics covered include weak measurements, quantum measurement reversal, quantum trajectories and the stochastic path integral formalism. The theory of quantum measurement is also covered in detail, including discussion of how it can be tested and demonstrated in a laboratory: how to build quantum-limited amplifiers, fundamental noise limits imposed on measurement by quantum mechanics, and the design of superconducting circuits. This text is an excellent introduction for students with a basic understanding of quantum mechanics wanting to learn more about measurement theory, and the inclusion of a wide selection of end-of-chapter exercises make this book ideal for emerging courses on the topic. Key chapters introducing the foundations of quantum computing and the history of measurement theory are equally accessible to a broader, less specialised audience.
In this chapter, the physical content of previous chapters is summarized, and the reader is suided towards some key areas of modern physics: the Feynman formulation, the unificaton of quantum theory with special relativity, and dualities in quantum mechanics. This very short chapter is intended to be a bridge aimed at motivating readers to attend first course in quantum field theory. Towards an overall view At this stage, the student or the general reader might want to know what picture of the physical world emerges from the material covered so far and from the areas related to it but not covered in our book, so as to be introduced to what is in sight not only for the beginner but also for the scientific community. For this purpose, we summarize very briefly the previous pictures and we arrive at three key concepts: the Lagrangian in quantum mechanics via the Feynman sum over histories; the unification of quantum mechanics and special relativity; and new duality symmetries in quantum mechanics. From Schrödinger to Feynman Quantum mechanics provides a probabilistic description of the world on atomic or sub-atomic scale. It tells us that, on such scales, the world can be described by a Hilbert space structure, or suitable generalizations. Even in the relatively simple case of the hydrogen atom, the appropriate Hilbert space is infinite-dimensional, but finite-dimensional Hilbert spaces play a role as well.