How Shor's Algorithm works (2007)
scottaaronson.com
scottaaronson.com
video lectures: http://web.de.mit.edu/public/courses/6/6.045/2015spring/
notes: http://stellar.mit.edu/S/course/6/sp15/6.045/materials.html
Here is a fantastic explanation of it: http://twistedoakstudios.com/blog/Post2644_grovers-quantum-s... [More technically involved explanation]
Interesting factoid: Scott Aaronson[2] interned with Lov Grover[3] at Bell Labs as a teenager!
[1] https://en.wikipedia.org/wiki/Grover%27s_algorithm
[2] https://blogs.scientificamerican.com/cross-check/scott-aaron... [This is a great interview, btw!]
These are some of the hardest papers to write and make visible; I was disabused of a few beliefs and the treatment of number theory didn't upset me so this was great, particularly the Fourier bit at the end.
Of course an algorithm like this is evergreen.
I am sorry for this derailing.