Quantum Fourier Transform Matrix for n-quibts
Part of my presentation for my Quantum Computing class today. The professor was so excited about my topic that he jumped up in the middle of my presentation and basically finished it for me.
Buggy Random Walk
Discrete Boundary Value Problem
The boundary value problem is a topic commonly covered in math methods courses physics majors must endure. It usually deals with solving differential equations over a highly symmetric geometries. It is taught because it is one of few precious victories in mankind’s futile attempt to describe the world using equations. A typical problem would be to show how temperature varies on a rectangular plate while certain edges are held at a constant value or what a vibrating string would look like over time.
Temperature of one side of plate is held at 1, the rest 0.
When the geometry gets tricky one trick to solving this problem would be to discretize the space of interest and make every point try to agree with its neighbors (average). The boundaries are special. They don’t have to agree with anyone.
Note the top and left edges aren’t random. This “consensus” method can take many iterations (everybody gets a say).
The mad dash to conformity is captured for the entertainment of the reader.