I've been watching David Deutsch's Lectures on Quantum Computation here
https://www.youtube.com/playlist?list=PLqdVnC7OWuEcfKRZXsrooK_EPzwmWSi-N
In Lecture 2, he gives these equations to show how X,Y and Z evolve where X,Y and Z are the Pauli matrices (https://youtu.be/ajgr58WN7A4?list=PLqdVnC7OWuEcfKRZXsrooK_EPzwmWSi-N&t=1441)
Z(t+1)=X(t)
Ÿ(t +1) = Y(t)
X(t+1)=-Z(t)
In lecture 4, he explains how these equations (which are gates) came from the main physical law, the Heisenberg equation of motion, and we can get the laws above by integrating the equation from t to t+1 https://youtu.be/BmbGNtSZa1o?list=PLqdVnC7OWuEcfKRZXsrooK_EPzwmWSi-N&t=428
This is the differential equation
dA(t)/dt = i[H,A(t)]. with H being a special matrix and the brackets denoting a commutator
I know basic algebra and calculus but I'm a bit stuck here since there are no examples or derivations attached to the lectures. I dont know how to integrate matrices.
Both Help and resources either on the math or the theory would be great!