Quantum Information & Computation Lecture 1: Introduction to Quantum Information and Computation

The following lecture is a series done by Xiang (Simba) Zou. It outlines the current state of quantum information and the frontiers of research in quantum information. First, Simba illustrates the rapidly growing nature of quantum information. Then, he talks about quantum supremacy and the possible downfall of RSA encryption. Afterward, Simba provides the mathematical prerequisite to understanding quantum information, namely linear algebra. Simultaneously, he outlines the physical significance of each of these objects in linear algebra. In particular, when discussing tensor products he emphasizes their importance in describing multi-particle systems. Finally, Simba and I had an enlightening discussion on Shor's algorithm and multi-entangled states.

Note: This channel is looking for more people to contribute talks, and we have a lot of theorists on the channel. I don't mind having more, but I would like some people doing experiments/computations to also talk about their work!

Chapters:
00:00 - How Simba and I met.
01:17 - Simba's self-introduction
02:51 - The reason for studying quantum information
03:59 - What to expect from this lecture series
05:15 - Disclaimers
06:13 - References
08:25 - Topics in this series
10:52 - Frontiers of quantum information research
11:48 - Quantum supremacy
13:27 - RSA encryption
14:23 - Shor's algorithm
14:59 - The fast-growing nature of quantum information
16:37 - Mathematical prerequisite
17:44 - Braket notation
19:14 - Defining vector spaces
22:07 - Basis vectors
24:47 - Linear operators
24:55 - Physical interpretation of linear operators
25:11 - Inner products
26:36 - Hilbert spaces
27:40 - Hermitian operators
29:15 - 2nd postulate of quantum mechanics
30:01 - Physical observables in quantum mechanics
31:33 - Simultaneous diagonalization theorem
31:48 - Commutators and anti-commutators
32:45 - Simultaneous diagonalization theorem (cont')
33:36 - Physical significance of simultaneous diagonalization theorem
36:04 - Tensor products
37:56 - Physical significance of tensor products
39:51 - Content of next lecture
40:25 - Comment on lecture
40:42 - Discussion of Shor's algorithm
41:40 - Discussion of multi-entangled states
47:42 - Minor comment on notation
48:11 - Funny discussion on vector spaces
48:44 - We need contributors