Titlebook: Introduction to Quantum Technologies; Alto Osada,Rekishu Yamazaki,Atsushi Noguchi Textbook 2022 The Editor(s) (if applicable) and The Auth

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Linear Algebrasfying the Schr?dinger equation. The wavefunction can be represented as a vector in a complex vector space called the Hilbert space. In quantum technology, we focus on manipulating the quantum state, where the vector in the Hilbert space is transformed and measured through various physical interacti

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Time Evolution in Quantum System computation, we apply sequences of quantum gates on qubits to perform calculations. It is important to be able to derive the time evolution of the system for a given system Hamiltonian and the external perturbations. In this chapter, we review the fundamentals of quantum mechanics focusing on the t

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Perturbation Theoryne of the most essential tools of quantum mechanics used to quantitatively determine the slight deviation in the quantum system due to external influences when their effects are sufficiently small. A few important results within the time-independent and time-dependent perturbation theory are introdu

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Harmonic Oscillatorrs, especially electromagnetic waves, are used in quantum technologies as indispensable tools as well. Actually, electromagnetic waves, for example, are principal tools for controlling quantum bits. Resonators for electromagnetic waves are often utilized for tailoring quantum bit-environment interac

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Two-level System and Interaction with Electromagnetic Wavests definition and representation using a Bloch sphere and then introduce the interaction between a qubit and a single harmonic oscillator, or Jaynes–Cummings interaction. On this basis, a governing equation of qubit dynamics subject to driving, e.g., the irradiation of electromagnetic waves is deriv

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Electromagnetic Cavities and Cavity Quantum Electrodynamicses, except for the photon itself as a quantum system. However, this is not the case when one wants to convert quantum states back and forth between a fixed quantum system and a photon, in a deterministic and efficient manner. For such a purpose, electromagnetic cavities, or electromagnetic resonator

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Various Couplings in Quantum Systemscoupling strengths in practice. The basic strategy is to consider classical interaction energies first, then quantize them to derive interaction Hamiltonians, and finally get the coupling strengths which include susceptibilities of the particles to an applied field and/or vacuum fluctuations of the

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Basics of Quantum Information Processing a set of single-qubit gates and at least one two-qubit gate allows for the preparation of an arbitrary quantum state. We put particular emphasis on the derivation of quantum gates from the physical Hamiltonians. The second idea is quantum measurement and quantum state/process tomography. Then we sc

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