1. Two-level quantum systems
1.1. Vectors and matrices
1.2. Foundation of quantum mechanics
1.3. Quantum state vectors
1.4. Non-cloning principle for qbit
1.5. Quantum entanglement
1.6. Another example of qbit
2. Universal gates
2.1. Classical universal gates
2.2. Alternative universal gates
2.3. NOT, CNOT, CCNOT, and Fredkin gates using spin states
3. Quantum logic gates
3.1. Introduction to quantum gate simulation
Blueqat for Python
3.2. Quantum gates
3.3. Controlled-unitary (controlled-U) gates
3.4. Half adder from quantum gates
4. Algorithms of quantum computation
4.1. Deutsch's algorithm
4.2. Grover's algorithm
4.3. Quantum Fourier transform
4.4. Phase estimation
4.5. Shor's algorithm for prime factorization
4.6. Simon's algorithm
4.7. Error corrections
5. Quantum information : entanglement and teleportation
5.1. Bell's inequality
5.2. Quantum teleportation
5.3. Superdense coding
6. Quantum cryptography (quantum key distribution)
6.1. Cryptography using a secret key
6.2. Photon-based qbit
6.3. BB84 protocol
Appendix A. Commercial quantum computers.