Recommended prerequisites:
05. Polarization: https://www.youtube.com/watch?v=RowMxWt4mVE
07. Introduction to quantum mechanics and quantum optics : https://www.youtube.com/watch?v=CfdpXSU-E_E

0:00 Overview and introduction

PHOTON POLARIZATION

2:43 Polarization states as two-level quantum systems
5:42 A comment on the meaning of 'superposition'
7:18 A comment on the meaning of the phase of a quantum coefficient
9:37 A comment on pure and mixed states: an analogy with partial polarization
11:44 Summary of the analogy between polarization states and two-level quantum systems

MULTI-PHOTON STATES

12:52 Describing the polarization state of a two-photon system: tensor product of vectors
14:22 Tensor product of operators
15:25 Unentangled and entangled states

GROVER'S ALGORITHM

18:47 Problem statement and classical solution
19:43 The solution using quantum computation
21:32 A more mathematical description of the algorithm
23:47 Some comments on the quantum physics behind the algorithm

SHOR'S ALGORITHM

24:37 Problem statement and overview of the solution
25:44 Mathematical reformulation of the problem
33:18 Period finding using quantum computation
36:08 Quantum Fourier transform
38:42 Approximating a fraction using continued fractions
40:06 Summary of Shor's algorithm