Ep 194: 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:    • How to Break Cryp...   and this video focussed more narrowly on Shor's algorithm:    • Hacking at Quantu...   2. Here is Peter Shor himself explaining the history of his work:    • The Story of Shor...   3. Artur Ekert's graduate level free online course on Quantum Information Theory: https://www.youtube.com/@ArturEkert/v... in particular his lecture focussed on Shor's Algorithm:    • IQIS Lecture 6.9 ...   (which, aside from "The Fabric of Reality" itself, served as the basis for this episode).