Topics covered in this chapter

1. 7.1. Introducing quantum bits
2. 7.2. Bras and kets
3. 7.3. The complex math and physics of a single qubit
   1. 7.3.1. Quantum state representation
   2. 7.3.2. Unitary matrices mapping to standard form
   3. 7.3.3. The density matrix
   4. 7.3.4. Observables and expectation
4. 7.4. A nonlinear projection
5. 7.5. The Bloch sphere
6. 7.6. Professor Hadamard, meet Professor Pauli
   1. 7.6.1. The quantum ID gate
   2. 7.6.2. The quantum X gate
   3. 7.6.3. The quantum Z gate
   4. 7.6.4. The quantum Y gate
   5. 7.6.5. The quantum H gate
   6. 7.6.6. The quantum Rφ gates
   7. 7.6.7. The quantum S gate
   8. 7.6.8. The quantum S† gate
   9. 7.6.9. The quantum T gate
   10. 7.6.10. The quantum T† gate
   ...