Hello Quantum Formalists,
For those who recently joined the community and don’t know where to start in terms of our courses, here are some tips/options;
1. Assuming you want to review or start with the basics around finite-dimensional Hilbert spaces, matrix operators and their underlying group structure U(n) & SU(n). Then start with what we called 'Foundation Module' - YouTube playlist via https://www.youtube.com/playlist?list=PL6N_Y7ao_aHsRGyruo9fg83rrBEg3S1nC. The module also covers the basic postulates of quantum mechanics, i.e. the correspondence between the physics concepts such as states & observables with the corresponding mathematical objects modelling these.
2. Assuming you are ok/comfortable with the topics in 1) as highlighted above, perhaps you want to start moving towards more advanced stuff such as Lie Groups, Lie Algebras & Representation Theory? If that's the case, then it is highly recommended that;
2. A. You audit the crash course on Topology & Differential Geometry via the playlist https://www.youtube.com/playlist?list=PL6N_Y7ao_aHs37APhitfR1SMX_VOqNDgj. In particular, try to understand the notion of a ‘smooth manifold’ because this is important when we get to Lie Groups in the summer. If our approach is too abstract, perhaps try to find other resources that are easier to digest smooth manifolds. Even if you are not interested in quantum computation, this stuff is also valuable for other applied topics such as ML, e.g. Geometric Deep Learning!
2. B. Take the crash course on Group Theory that has just recently started. Playlist for the lectures https://www.youtube.com/playlist?list=PL6N_Y7ao_aHuOMgD3T_dzSgM5E2-VhhbT. The next live session (lecture 2) will be this Friday at 5pm GMT, and the registration to attend is https://www.crowdcast.io/e/group-theory-lecture-02. This crash course is also helpful if you are interested in ML and Cryptography!
That's it for today. Happy rest of the week!
Bambordé