Season 10 Episode 1

Anjali is back on the Oxford Online Maths Club to tell us about logic gates in both classical mechanics and in quantum mechanics, using complex numbers and matrices.

Watch on YouTube

Further Reading

Books and Courses

Anjali recommends the Oxford course C7.4 Introduction to Quantum Information, currently taught by Prof. Artur Ekert. You might like to click the link to see what the course is like, but it's a fourth-year (graduate-level) mathematics course, and it's designed for people who have already taken several university 

There's also a series of videos with Artur Ekert talking through some of the course material, which might be a little bit more accessible.

Coincidentally, 3Blue1Brown published a video on the same day as us about Quantum Information. They also posted a follow-up video re-explaining a tricky bit of that video.

Prof. Bob Coecke is a CS professor at Oxford. Together with one of his students, he’s written a book called Quantum in Pictures (Bob Coecke and Stefano Gogioso) that’s about the quantum logic gates that Anjali was getting towards at the end of the livestream. These diagrams form something called the ZX-Calculus, which includes a collection of rules for manipulating these diagrams.

Complex Numbers in Quantum Mechanics

Quantum mechanics is very strange. On the livestream, we briefly discussed the fact that complex numbers are used for the amplitudes, even though it’s only the magnitude of that complex number that affects the probability that the system is observed to be in a particular state. The Aharonov–Bohm effect is an experimental demonstration that the complex phase does, nevertheless, matter. That’s putting it lightly; the Aharonov-Bohm effect also demonstrates non-locality. You might also like Bell's Theorem. Quantum mechanics is very very strange.