David Deutsch’s ”The Fabric of Reality” Chapter 9 ”Quantum Computers” Part 4: Shor's Algorithm

This is a "return to regular format" episode in one respect - readings from and reflections upon "The Fabric of Reality" but also a departure from regular formatting in another respect: I teach a bunch of simple mathematics. This is for those who might think "quantum computation" and "quantum algorithms" will be forever beyond me. They are not! I begin with (quite literally) primary school mathematics level stuff (what's a prime number, what is the "fundamental theorem of arithmetic") and very gradually move up into algebra and some modular arithmetic and present examples using real numbers of what the *problem* is and then lead us to a place where we can glimpse the solution (which is Shor's Algorithm). I do not promise to bring the listener to a graduate quantum physics-degree-level of proficiency in quantum information theory and cryptography - but you will gain quite some insight. I refer to the following more in-depth expositions of all this and hopefully bridge the gap I think is there between "I know a little bit of maths and physics" and the kind of thing the following more "high level" videos offer (which I present in order of increasing technical difficulty)

1. The PBS Infinite Series on all this stuff is brilliant. In particular this introduction: https://www.youtube.com/watch?v=12Q3Mrh03Gk and this video focussed more narrowly on Shor's algorithm: https://www.youtube.com/watch?v=wUwZZaI5u0c

2. Here is Peter Shor himself explaining the history of his work: https://www.youtube.com/watch?v=6qD9XElTpCE

3. Artur Ekert's graduate level free online course on Quantum Information Theory: https://www.youtube.com/@ArturEkert/videos in particular his lecture focussed on Shor's Algorithm: https://www.youtube.com/watch?v=TioipZX7d5U (which, aside from "The Fabric of Reality" itself, served as the basis for this episode).