| [NT 15003449]: |
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 -- 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. |