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.