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This book is a concise primer of quantum technology aiming at providing a comprehensive material of fundamentals to help beginners understand the common concepts and background theories to technologies for individual quantum systems. Further, it also describes how the concepts and theories are applied to technologies in various systems.
This book consists of three parts. The first part looks back over basics of quantum mechanics necessary for the main content, including quantum state and operators, time evolution and perturbation theory. The second part explains in detail key components indispensable to follow quantum technologies: two-level systems, harmonic oscillator and cavity quantum electrodynamics and resonators. In the third part, the physical quantum systems are treated in a more abstract way by introducing quantum logic gates, quantum measurement and quantum error correction. Technical supplements are included in Appendices.
The well-compiled topics and concise presentation feature the book as a supplemental primer in the courses of quantum technologies including quantum computing, quantum communication, quantum sensing and quantum simulation.
What is quantum technology? Is it a fancy bandwagon fresh from the academics? Definitely, this is not the case. Let us trace the history in reverse order from 2022. Now the quantum technology is known to everybody, thanks to the many-qubit quantum “computers” developed by several companies and laboratories. Some of them are available on the cloud platform and are used for the educational and business use, while quantum communication and quantum sensing/metrology are also under intense investigation. Why does quantum computer gather such an attention? An answer is that such a novel computer based on the unconventional working principle—quantum mechanics—is expected to outperform conventional computers, or classical computers as a counterpart of the quantum computer, when a certain computational task is given.
We would like to stress that this very work ignited the experimental exploration of quantum computer which had been distinguished from a mere analog computer intolerable to errors occurring in an analog manner as well. To date, a number of breathtaking progress have been made in various quantum systems, especially in ion-trap and superconducting-circuit systems.
Quantum States and Quantum Mechanics
Quantum States and Quantum Mechanics
Linear Algebra
Wavefunction and Notations in Quantum Mechanics
Time Evolution in Quantum System
Perturbation Theory
Harmonic Oscillator, Qubit and Coupled Quantum Systems
Harmonic Oscillator
Two-level System and Interaction with Electromagnetic Waves
Electromagnetic Cavities and Cavity Quantum Electrodynamics
Various Couplings in Quantum Systems
Quantum Information Processing and Quantum Technologies
Basics of Quantum Information Processing
Quantum Technologies
Appendix A: Position and Momentum Representations
Appendix B: Unitary Transformation to a Rotating Frame
Appendix C: Extraction of a Two-Level System from a Three-Level System
Appendix D: Quantum Theory of Hydrogen Atom
Appendix E: Master Equation
Appendix F: Schrieffer–Wolff Transformation
Appendix G: Derivation of the SWAP Gate from the Heisenberg Hamiltonian
Appendix H: Cavity Cooling of a Mechanical Mode
Appendix I: Entangled States and Quantum Teleportation
Appendix J: Quantum No-Cloning Theorem