Quantum Computing: Fundamentals and Applications

This lecture covers the fundamentals of quantum computing, including qubit realization, scalable quantum computers, quantum communication, sensing, and metrology. It delves into basic concepts such as qubits, superposition, measurement, gates, Bloch sphere, unitary transforms, quantum algorithms, and quantum arithmetic. The lecture also explores the Bloch sphere, its definition, derivation, properties, and applications in quantum computing. It discusses the normalization constraint, global phase invariance, qubit states, and the encoding of functions into unitaries. Moreover, it introduces higher-qubit gates, Toffoli gate, controlled-NOT gate, controlled-phase gate, and quantum parallelism. The lecture concludes with an overview of quantum algorithms, including the Deutsch algorithm and the Grover algorithm.

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In quantum computing, a qubit (ˈkjuːbɪt) or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization.

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