Visualizing Complex Numbers & QFT

Visualizing complex numbers and complex functions

We can colour the complex plane, so black is at the origin, white is at infinity, and the rainbow circles the origin


Then, a function can be plotted by putting the colour of the OUTPUT at each INPUT location

To read this: black holes are zeroes, white areas are large in absolute value, red areas are positive real, turquoise is negative real.


Here is a picture of the Quantum Fourier Transform matrix

The entries of the matrix are coloured as complex numbers. Change N to get bigger/smaller matrix.


Next two boxes: define a function and then take its QFT visually

First, in this box, define and graph a function.

Next, in this box, show its QFT. Rainbow colours for argument (angle), magnitude is plotted vertically.

Here’s another QFT visualizer I wrote.

Initialize a Complex Matrix Plotter


Plot the QFT with it


The states of two qubits, first few steps of Shor


An extra box