08. Photon polarization and quantum computing (Shor's algorithm, Grover's algorithm) |
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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 |