Introduction to Quantum Computing

<p>The Most Important Step to Understand Quantum Computing.- First Impression.- Basis, Basis Vectors, and Inner Product.- Orthonormal Basis, Bra-Ket Notation, and Measurement.- Changing Basis, Uncertainty Principle, and Bra-ket Operations.- Observables, Operators, Eigenvectors, and Eigenvalues.- Pauli Spin Matrices, Adjoint Matrix, and Hermitian Matrix.- Operator Rules, Real Eigenvalues, and Projection Operator.- Eigenvalue and Matrix Diagonalization; Unitary Matrix.- Unitary Transformation, Completeness, and Construction of Operator.- Hilbert Space, Tensor Product, and Multi-Qubit.- Tensor Product of Operators, Partial Measurement, and Matrix Representation in a Given Basis.- Quantum Register and Data Processing, Entanglement and the Bell States.- Concepts Review, Density Matrix, and Entanglement Entropy.- Quantum Gate Introduction; NOT and C-NOT Gates.- SWAP, Phase Shift and CC-NOT (Toffoli) Gates.- Walsh-Hadamard Gate and its Properties.-&nbsp;Two Quantum Circuit Examples.- No-Cloning Theorem and Quantum Teleportation I.- Quantum Teleportation II and Entanglement Swapping.- Deutsch Algorithm.- Quantum Oracles and Construction of Quantum Gate.- Grover’s Algorithm: I.- Grover’s Algorithm: II.- Quantum Fourier Transform I.- Quantum Fourier Transform II.- Bloch Sphere and Single-Qubit Arbitrary Unitary Gate.- Quantum Phase Estimation.- Shor’s Algorithm.- The Last But Not the Least..</p>